id large_stringlengths 9 16 | title large_stringlengths 1 382 | abstract large_stringlengths 3 6.09k | publish_date date32 | update_date date32 | categories large listlengths 1 13 | authors large_stringlengths 3 62.8k |
|---|---|---|---|---|---|---|
math/9309210 | Bounds on the tail probability of U-statistics and quadratic forms | The authors announce a general tail estimate, called a decoupling inequality,
for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent
random variables. | 1993-09-13 | 2016-09-06 | [
"math.FA",
"math.PR"
] | Victor H. de la Pe\~na, Stephen J. Montgomery-Smith |
math/9309211 | Decoupling Inequalities for the Tail Probabilities of Multivariate
U-statistics | In this paper the following result, which allows one to decouple U-Statistics
in tail probability, is proved in full generality.
Theorem 1. Let $X_i$ be a sequence of independent random variables taking
values in a measure space $S$, and let $f_{i_1...i_k}$ be measurable functions
from $S^k$ to a Banach space $B$. Le... | 1993-09-13 | 2008-02-03 | [
"math.FA"
] | Victor H. de la Pe\~na, Stephen J. Montgomery-Smith |
math/9308207 | Regular operators between non-commutative $L_p$-spaces | We introduce the notion of a regular mapping on a non-commutative $L_p$-space
associated to a hyperfinite von Neumann algebra for $1\le p\le \infty$. This is
a non-commutative generalization of the notion of regular or order bounded map
on a Banach lattice. This extension is based on our recent paper [P3], where we
int... | 1993-08-24 | 2016-09-06 | [
"math.FA"
] | Gilles Pisier |
math/9308208 | Bilinear forms on exact operator spaces and B(H)\otimes B(H) | Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra
$K(H)$ of all the compact operators on an infinite dimensional Hilbert space
$H$). We study a class of bounded linear maps $u\colon E\to F^*$ which we call
tracially bounded. In particular, we prove that every completely bounded (in
short $c.b.$) ... | 1993-08-24 | 2016-09-06 | [
"math.FA"
] | Marius Junge, Gilles Pisier |
math/9308206 | The $M$-ideal structure of some algebras of bounded linear operators | Let $1<p,\,q<\infty$. It is shown for complex scalars that there are no
nontrivial $M$-ideals in $L(L_p[0,1])$ if $p\neq 2$, and $K(\ell_p(\ell_q^n)$
is the only nontrivial $M$-ideal in $L(\ell_p(\ell_q^n)$. This proves a
conjecture of C.-M. Cho and W. B. Johnson. | 1993-08-13 | 2008-02-03 | [
"math.FA"
] | Nigel J. Kalton, Dirk Werner |
math/9308205 | On impossible extensions of Krivine's Theorem | We give examples of two Banach spaces. One Banach space has no spreading
model which contains $\ell_p$ ($1\le p<\infty$) or $c_0$. The other space has
an unconditional basis for which $\ell_p$ ($1\le p<\infty$) and $c_0$ are block
finitely represented in all block bases. | 1993-08-10 | 2016-09-06 | [
"math.FA"
] | Edward Odell, Thomas Schlumprecht |
math/9308204 | Exact operator spaces | In this paper, we study {\it operator spaces\/} in the sense of the theory
developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an
operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert.
We will be mainly concerned here with the ``geometry'' of {\it finite
dimensional\/} operator ... | 1993-08-09 | 2016-09-06 | [
"math.FA"
] | Gilles Pisier |
math/9307201 | Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces | We present a spectral mapping theorem for continuous semigroups of operators
on any Banach space $E$. The condition for the hyperbolicity of a semigroup on
$E$ is given in terms of the generator of an evolutionary semigroup acting in
the space of $E$-valued functions. The evolutionary semigroup generated by the
propaga... | 1993-07-08 | 2008-02-03 | [
"math.FA"
] | Yuri D. Latushkin, Stephen J. Montgomery-Smith |
math/9306210 | Some stability properties of $c_0$-saturated spaces | A Banach space is $c_0$-saturated if all of its closed infinite dimensional
subspaces contain an isomorph of $c_0$. In this article, we study the stability
of this property under the formation of direct sums and tensor products. Some
of the results are: (1) a slightly more general version of the fact that
$c_0$-sums of... | 1993-06-21 | 2016-09-06 | [
"math.FA"
] | Denny H. Leung |
math/9306212 | A remark about distortion | In this note we show that every Banach space $X$ not containing $\ell_1^n$
uniformly and with unconditional basis contains an arbitrarily distortable
subspace. | 1993-06-21 | 2009-09-25 | [
"math.FA"
] | Bernard Maurey |
math/9306211 | Banach spaces without local unconditional structure | For a large class of Banach spaces, a general construction of subspaces
without local unconditional structure is presented. As an application it is
shown that every Banach space of finite cotype contains either $l_2$ or a
subspace without unconditional basis, which admits a Schauder basis. Some other
interesting applic... | 1993-06-21 | 2016-09-06 | [
"math.FA"
] | R. Komowski, Nicole Tomczak-Jaegermann |
math/9306209 | The k_t--functional for the interpolation couple
L^\infty(d\mu;L^1(d\nu)), L^\infty(d\nu;L^1(d\mu)) | Let $(M,\mu)$ and $(N,\nu)$ be measure spaces. In this paper, we study the
$K_t$--\,functional for the couple $$A_0=L^\infty(d\mu\,;
L^1(d\nu))\,,~~A_1=L^\infty(d\nu\,; L^1(d\mu))\,. $$
Here, and in what follows the vector valued $L^p$--\,spaces $L^p(d\mu\,;
L^q(d\nu))$ are meant in Bochner's sense.
One of our main... | 1993-06-09 | 2016-09-06 | [
"math.FA"
] | Albrecht Hess, Gilles Pisier |
math/9306208 | Isometric stability property of certain Banach spaces | Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach
space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that
$E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if
$E$ is isometric to a subspace of $F.$ Moreover, every isometry $T$ from $E$
into $L_p(... | 1993-06-09 | 2016-09-06 | [
"math.FA"
] | Alexander Koldobsky |
math/9306207 | Complex Interpolation and Regular Operators Between Banach | We study certain interpolation and extension properties of the space of
regular operators between two Banach lattices. Let $R_p$ be the space of all
the regular (or equivalently order bounded) operators on $L_p$ equipped with
the regular norm. We prove the isometric identity $R_p = (R_\infty,R_1)^\theta$
if $\theta = 1... | 1993-06-07 | 2016-09-06 | [
"math.FA"
] | Gilles Pisier |
math/9306206 | Noncommutative vector valued $L_p$-spaces and completely $p$-summing
maps | Let $E$ be an operator space in the sense of the theory recently developed by
Blecher-Paulsen and Effros-Ruan. We introduce a notion of $E$-valued non
commutative $L_p$-space for $1 \leq p < \infty$ and we prove that the resulting
operator space satisfies the natural properties to be expected with respect to
e.g. duali... | 1993-06-07 | 2016-09-06 | [
"math.FA"
] | Gilles Pisier |
math/9305203 | Random Banach spaces. The limitations of the method | We study the properties of "generic", in the sense of the Haar measure on the
corresponding Grassmann manifold, subspaces of l^N_infinity of given dimension.
We prove that every "well bounded" operator on such a subspace, say E, is a
"small" perturbation of a multiple of identity, where "smallness" is defined
intrinsic... | 1993-05-11 | 2016-09-06 | [
"math.FA"
] | P. Mankiewicz, Stanislaw J. Szarek |
math/9304213 | Prevalence: an addendum | The authors mention work of Christensen, Mycielski, Tsujii, and others which
is closely related to a survey article by the first author [math.FA/9210220]. | 1993-04-01 | 2008-02-03 | [
"math.FA",
"math.DS"
] | Brian R. Hunt, Tim Sauer, James A. Yorke |
math/9304206 | Some isomorphically polyhedral Orlicz sequence spaces | A Banach space is polyhedral if the unit ball of each of its finite
dimensional subspaces is a polyhedron. It is known that a polyhedral Banach
space has a separable dual and is $c_0$-saturated, i.e., each closed infinite
dimensional subspace contains an isomorph of $c_0$. In this paper, we show that
the Orlicz sequenc... | 1993-04-01 | 2016-09-06 | [
"math.FA"
] | Denny H. Leung |
math/9303203 | W^*-derived sets of transfinite order of subspaces of dual Banach spaces | It is an English translation of the paper originally published in Russian and
Ukrainian in 1987. In the appendix of his book S.Banach introduced the
following definition Let $X$ be a Banach space and $\Gamma$ be a subspace of
the dual space $X^*$. The set of all limits of $w^{*}$-convergent sequences in
$\Gamma $ is ca... | 1993-03-29 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9303206 | Total subspaces with long chains of nowhere norming weak$^*$ sequential
closures | If a separable Banach space $X$ is such that for some nonquasireflexive
Banach space $Y$ there exists a surjective strictly singular operator $T:X\to
Y$ then for every countable ordinal $\alpha $ the dual of $X$ contains a
subspace whose weak$^*$ sequential closures of orders less than $\alpha $ are
not norming over an... | 1993-03-29 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9303205 | A note on analytical representability of mappings inverse to integral
operators | The condition onto pair ($F,G$) of function Banach spaces under which there
exists a integral operator $T:F\to G$ with analytic kernel such that the
inverse mapping $T^{-1}:$im$T\to F$ does not belong to arbitrary a priori given
Borel (or Baire) class is found. | 1993-03-29 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9303204 | Total subspaces in dual Banach spaces which are not norming | The main result: the dual of separable Banach space $X$ contains a total
subspace which is not norming over any infinite dimensional subspace of $X$ if
and only if $X$ has a nonquasireflexive quotient space with the strictly
singular quotient mapping. | 1993-03-29 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9303202 | Topologies on the set of all subspaces of a banach space and related
questions of banach space geometry | For a Banach space $X$ we shall denote the set of all closed subspaces of $X$
by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$
with a topology. The main purpose of the present paper is to survey results on
two the most common topologies on $G(X)$. | 1993-03-29 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9303201 | Spaces Of Lipschitz Functions On Banach Spaces | A remarkable theorem of R. C. James is the following: suppose that $X$ is a
Banach space and $C \subseteq X$ is a norm bounded, closed and convex set such
that every linear functional $x^* \in X^*$ attains its supremum on $C$; then
$C$ is a weakly compact set. Actually, this result is significantly stronger
than this s... | 1993-03-04 | 2016-09-06 | [
"math.FA"
] | Charles P. Stegall |
math/9302216 | Lyapunov theorems for Banach spaces | We present a spectral mapping theorem for semigroups on any Banach space $E$.
From this, we obtain a characterization of exponential dichotomy for
nonautonomous differential equations for $E$-valued functions. This
characterization is given in terms of the spectrum of the generator of the
semigroup of evolutionary oper... | 1993-02-24 | 2016-09-06 | [
"math.FA",
"math.SP"
] | Yuri Latushkin, Stephen Montgomery-Smith |
math/9302214 | Bounded linear operators between C^*-algebras | Let $u:A\to B$ be a bounded linear operator between two $C^*$-algebras $A,B$.
The following result was proved by the second author.
Theorem 0.1. There is a numerical constant $K_1$ such that for all finite
sequences $x_1,\ldots, x_n$ in $A$ we have
$$\leqalignno{&\max\left\{\left\|\left(\sum u(x_i)^*
u(x_i)\right)^{1... | 1993-02-18 | 2016-09-06 | [
"math.FA"
] | U. Haagerup, Gilles Pisier |
math/9302215 | Projections from a von~Neumann algebra onto a subalgebra | This paper is mainly devoted to the following question:\ Let $M,N$ be
von~Neumann algebras with $M\subset N$, if there is a completely bounded
projection $P\colon \ N\to M$, is there automatically a contractive projection
$\widetilde P\colon \ N\to M$?
We give an affirmative answer with the only restriction that $M$ ... | 1993-02-18 | 2009-09-25 | [
"math.FA"
] | Gilles Pisier |
math/9302213 | A factorization constant for $l^n_p | We prove that if PT is a factorization of the identity operator on \ell_p^n
through \ell_{\infty}^k, then ||P|| ||T|| \geq Cn^{1/p-1/2}(log n)^{-1/2}. This
is a corollary of a more general result on factoring the identity operator on a
quasi-normed space through \ell_{\infty}^k. | 1993-02-11 | 2016-09-06 | [
"math.FA"
] | N. Tenney Peck |
math/9302212 | Dual Kadec-Klee norms and the relationships between Wijsman, slice and
Mosco convergence | In this paper, we completely settle several of the open questions regarding
the relationships between the three most fundamental forms of set convergence.
In particular, it is shown that Wijsman and slice convergence coincide
precisely when the weak star and norm topologies agree on the dual sphere.
Consequently, a wea... | 1993-02-09 | 2016-09-06 | [
"math.FA"
] | Jonathan M. Borwein, J. Vanderwerff |
math/9302211 | Locally Lipschitz Functions and Bornological Derivatives | We study the relationships between Gateaux, weak Hadamard and Frechet
differentiability and their bornologies for Lipschitz and for convex functions.
In particular, Frechet and weak Hadamard differentiabily coincide for all
Lipschitz functions if and only if the space is reflexive (an earlier paper of
the first two aut... | 1993-02-09 | 2016-09-06 | [
"math.FA"
] | Jonathan M. Borwein, Marian Fabian, J. Vanderwerff |
math/9302207 | How many vectors are needed to compute (p,q)-summing norms? | We will show that for $q<p$ there exists an $\al < \infty$ such that \[
\pi_{pq}(T) \pl \le c_{pq} \pi_{pq}^{[n^{\alpha}]}(T) \mbox{for all $T$ of rank
$n$.}\] Such a polynomial number is only possible if $q=2$ or $q<p$.
Furthermore, the growth rate is linear if $q=2$ or
$\frac{1}{q}-\frac{1}{p}>\frac{1}{2}$. Unless
$\... | 1993-02-04 | 2016-09-06 | [
"math.FA"
] | M. Defant, Marius Junge |
math/9302208 | Every nonreflexive subspace of L_1[0,1] fails the fixed point property | The main result of this paper is that every non-reflexive subspace $Y$ of
$L_1[0,1]$ fails the fixed point property for closed, bounded, convex subsets
$C$ of $Y$ and nonexpansive (or contractive) mappings on $C$. Combined with a
theorem of Maurey we get that for subspaces $Y$ of $L_1[0,1]$, $Y$ is reflexive
if and onl... | 1993-02-04 | 2016-09-06 | [
"math.FA"
] | Paddy N. Dowling, Christopher J. Lennard |
math/9302209 | Lectures on maximal monotone operators | This is a 30 page set of lecture notes, in Plain TeX, which were prepared for
and presented as a series of lectures (10 1/2 hours over two weeks) at the 2nd
Summer School on Banach Spaces, Related Areas and Applications in Prague and
Paseky, Czech Republic, during August, 1993. They consist of a largely
self-contained ... | 1993-02-04 | 2016-09-06 | [
"math.FA"
] | Robert R. Phelps |
math/9302206 | Comparing gaussian and Rademacher cotype for operators on the space of
continous functions | We will prove an abstract comparision principle which translates gaussian
cotype in Rademacher cotype conditions and vice versa. More precisely, let
$2\!<\!q\!<\!\infty$ and $T:\,C(K)\,\to\,F$ a linear, continous operator.
T is of gaussian cotype q if and only if
( \summ_1^n (\frac{|| Tx_k||_F}{\sqrt{\log(k+1)}})^q... | 1993-02-04 | 2016-09-06 | [
"math.FA"
] | Marius Junge |
math/9302205 | Twisted sums and a problem of Klee | Let F be a quasi-linear map on a separable normed space X, and assume that F
splits on an infinite-dimensional subspace of X. Then the twisted sum topology
induced by F on the direct sum of X and the real line can be written as the
supremum of a nearly convex topology and a trivial dual topology. (This
partially answer... | 1993-02-03 | 2008-02-03 | [
"math.FA"
] | N. Tenney Peck |
math/9302204 | The Complete Continuity Property and Finite Dimensional Decompositions | A Banach space $\X$ has the complete continuity property (CCP) if each
bounded linear operator from $L_1$ into $\X$ is completely continuous (i.e.,
maps weakly convergent sequences to norm convergent sequences). The main
theorem shows that a Banach space failing the CCP (resp., failing the CCP and
failing cotype) has a... | 1993-02-02 | 2008-02-03 | [
"math.FA"
] | Maria Girardi, William B. Johnson |
math/9301201 | A Uniform Kadec-klee Property For Symmetric Operator Spaces | We show that if a rearrangement invariant Banach function space $E$ on the
positive semi-axis satisfies a non-trivial lower $q-$ estimate with constant
$1$ then the corresponding space $E(\nm)$ of $\tau-$measurable operators,
affiliated with an arbitrary semi-finite von Neumann algebra $\nm$ equipped
with a distinguish... | 1993-01-28 | 2016-09-06 | [
"math.FA"
] | Peter G. Dodds, T. K. Dodds, Paddy N. Dowling, Christopher J. Lennard,
Fyodor A. Sukochev |
math/9311201 | The Geometry of Cycles in the Cayley Diagram of a Group | A study of triangulations of cycles in the Cayley diagrams of finitely
generated groups leads to a new geometric characterization of hyperbolic
groups. | 1993-11-02 | 2008-02-03 | [
"math.GR"
] | Robert H. Gilman |
math/9310209 | A bicombing that implies a sub-exponential isoperimetric inequality | The idea of applying isoperimetric functions to group theory is due to
M.Gromov. We introduce the concept of a ``bicombing of narrow shape'' which
generalizes the usual notion of bicombing. Our bicombing is related to but
different from the combings defined by M. Bridson. If the Cayley graph of a
group with respect to ... | 1993-10-23 | 2008-02-03 | [
"math.GR"
] | Guenther Huck and Stephan Rosebrock |
math/9310207 | Projective resolutions for graph products | Let $\Gamma$ be a finite graph together with a group $G_v$ at each vertex
$v$. The graph product $G(\Gamma)$ is obtained from the free product of all
$G_v$ by factoring out by the normal subgroup generated by $\{g^{-1}h^{-1}gh;
g\in G_v, h\in G_w\}$ for all adjacent $v,w$. In this note we construct a
projective resolut... | 1993-10-16 | 2009-09-25 | [
"math.GR"
] | Daniel E. Cohen |
math/9310208 | Isoperimetric functions for graph products | Let $\Gamma$ be a finite graph, and for each vertex $i$ let $G_i$ be a
finitely presented group. Let $G$ be the graph product of the $G_i$. That is,
$G$ is the group obtained from the free product of the $G_i$ by factoring out
by the smallest normal subgroup containing all $[g,h]$ where $g\in G_i$ and
$h\in G_j$ and th... | 1993-10-16 | 2008-02-03 | [
"math.GR"
] | Daniel E. Cohen |
math/9310206 | Products of Commutators and Products of Squares in a Free Group | A classification of the ways in which an element of a free group can be
expressed as a product of commutators or as a product of squares is given. This
is then applied to some particular classes of elements. Finally, a question
about expressing a commutator as a product of squares is addressed. | 1993-10-15 | 2008-02-03 | [
"math.GR"
] | Leo P. Comerford Jr. and Charles C. Edmunds |
math/9310205 | Commutators as Powers in Free Products of Groups | The ways in which a nontrivial commutator can be a proper power in a free
product of groups are identified. | 1993-10-15 | 2008-02-03 | [
"math.GR"
] | Leo P. Comerford Jr., Charles C. Edmunds and Gerhard Rosenberger |
math/9310204 | Cogrowth and essentiality in groups and algebras | The cogrowth of a subgroup is defined as the growth of a set of coset
representatives which are of minimal length. A subgroup is essential if it
intersects non-trivially every non-trivial subgroup. The main result of this
paper is that every function $f:{\Bbb N}\cup \{0\}\rightarrow {\Bbb N}$ which
is strictly increasi... | 1993-10-14 | 2008-02-03 | [
"math.GR"
] | Amnon Rosenmann |
math/9310202 | The Bieri-Neumann-Strebel invariants for graph groups | Given a finite simplicial graph ${\cal G}$, the graph group $G{\cal G}$" is
the group with generators in one-to-one correspondence with the vertices of
${\cal G}$ and with relations stating two generators commute if their
associated vertices are adjacent in ${\cal G}$. The Bieri-Neumann-Strebel
invariant can be explici... | 1993-10-12 | 2009-09-25 | [
"math.GR"
] | John Meier and Leonard Vanwyk |
math/9310203 | Unions of Cockroft two-complexes | A combinatorial group-theoretic hypothesis is presented that serves as a
necessary and sufficient condition for a union of connected Cockcroft
two-complexes to be Cockcroft. This hypothesis has a component that can be
expressed in terms of the second homology of groups. The hypothesis is applied
to the study of the thi... | 1993-10-12 | 2009-09-25 | [
"math.GR"
] | William A. Bogley |
math/9306203 | Sur un generalisation del notion de producto libere amalgamate de
gruppos | In ``A remark about the description of free products of groups'', Proc.
Cambgridge Philos. Soc 62(1966), io ha studite lo que occurre in le
circumstantia que un gruppo $G$ ha un subensemble $P$ tal que tote elemento de
$G$ es representabile unicamente per un verbo reducite in $P$. Il eveni que tal
$P$ es multo como un ... | 1993-06-16 | 2016-09-06 | [
"math.GR"
] | John R. Stallings |
math/9306204 | A note on Context Sensitive languages and Word Problems | Anisimov and Seifert show that a group has a regular word problem ifand only
if it is finite. Muller and Schupp (together with Dunwoody's accessibility
result) show that a group has context free word problem if and only if it is
virtually free. In this note, we exhibit a class of groups where the word
problem is as clo... | 1993-06-16 | 2008-02-03 | [
"math.GR"
] | Michael Shapiro |
math/9306205 | Automatic structures and boundaries for graphs of groups | We study the synchronous and asynchronous automatic structures on the
fundamental group of a graph of groups in which each edge group is finite. Up
to a natural equivalence relation, the set of biautomatic structures on such a
graph product bijects to the product of the sets of biautomatic structures on
the vertex grou... | 1993-06-16 | 2008-02-03 | [
"math.GR"
] | Walter D. Neumann and Michael Shapiro |
math/9306202 | Almost Convex Groups and the Eight Geometries | If $M$ is a closed Nil geometry 3-manifold then $\pi_1(M)$ is almost convex
with respect to a fairly simple ``geometric'' generating set. If $G$ is a
central extension or a ${\Bbb Z}$-extension of a word hyperbolic group, then
$G$ is also almost convex with respect to some generating set. Combining these
with previousl... | 1993-06-16 | 2008-02-03 | [
"math.GR"
] | Michael Shapiro and Melany Stein |
math/9306201 | (p,q,r)-Generations for Janko Groups $J_1$ and $J_2$ | No abstract is available | 1993-06-10 | 2009-09-25 | [
"math.GR"
] | Jamshid Moori |
math/9305201 | Musings on Magnus | The object of this paper is to describe a simple method for proving that
certain groups are residually torsion-free nilpotent, to describe some new
parafree groups and to raise some new problems in honour of the memory of
Wilhelm Magnus. | 1993-05-26 | 2009-09-25 | [
"math.GR"
] | Gilbert Baumslag |
math/9307228 | Topological invariance of intersection lattices of arrangements in CP^2 | Let $\scr A^*=\{l_1,l_2,\cdots,l_n\}$ be a line arrangement in $\Bbb{CP}^2$,
i.e., a collection of distinct lines in $\Bbb{CP}^2$. Let $L(\scr A^*)$ be the
set of all intersections of elements of $A^*$ partially ordered by $X\leq
Y\Leftrightarrow Y\subseteq X$. Let $M(\scr A^*)$ be $\Bbb{CP}^2-\bigcup\scr
A^*$ where $\... | 1993-07-01 | 2009-09-25 | [
"math.GT",
"math.AG"
] | Tan Jiang, Stephen S.-T. Yau |
math/9307230 | The genus-minimizing property of algebraic curves | A viable and still unproved conjecture states that, if $X$ is a smooth
algebraic surface and $C$ is a smooth algebraic curve in $X$, then $C$ realizes
the smallest possible genus amongst all smoothly embedded $2$-manifolds in its
homology class. A proof is announced here for this conjecture, for a large
class of surfac... | 1993-07-01 | 2016-09-06 | [
"math.GT",
"math.DG"
] | Peter B. Kronheimer |
math/9307233 | Quasipositivity as an obstruction to sliceness | For an oriented link $L \subset S^3 = \Bd\!D^4$, let $\chi_s(L)$ be the
greatest Euler characteristic $\chi(F)$ of an oriented 2-manifold $F$ (without
closed components) smoothly embedded in $D^4$ with boundary $L$. A knot $K$ is
{\it slice} if $\chi_s(K)=1$. Realize $D^4$ in $\C^2$ as
$\{(z,w):|z|^2+|w|^2\le1\}$. It h... | 1993-07-01 | 2008-02-03 | [
"math.GT"
] | Lee Rudolph |
math/9304210 | Topology of homology manifolds | We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$,
with arbitrary resolution obstruction, homotopy equivalent to any simply
connected, closed $n$-manifold. We further investigate the structure of
generalized manifolds and present a program for understanding their topology. | 1993-04-01 | 2009-09-25 | [
"math.GT"
] | John L. Bryant, Steven C. Ferry, Washington Mio, Shmuel Weinberger |
math/9304209 | New points of view in knot theory | In this article we shall give an account of certain developments in knot
theory which followed upon the discovery of the Jones polynomial in 1984. The
focus of our account will be recent glimmerings of understanding of the
topological meaning of the new invariants. A second theme will be the central
role that braid the... | 1993-04-01 | 2009-09-25 | [
"math.GT"
] | Joan S. Birman |
math/9301212 | M\"obius invariance of knot energy | A physically natural potential energy for simple closed curves in $\bold R^3$
is shown to be invariant under M\"obius transformations. This leads to the
rapid resolution of several open problems: round circles are precisely the
absolute minima for energy; there is a minimum energy threshold below which
knotting cannot ... | 1993-01-01 | 2016-09-06 | [
"math.GT"
] | Steve Bryson, Michael H. Freedman, Zheng-Xu He, Zhenghan Wang |
math/9307227 | ``Theoretical mathematics'': Toward a cultural synthesis of mathematics
and theoretical physics | Is speculative mathematics dangerous? Recent interactions between physics and
mathematics pose the question with some force: traditional mathematical norms
discourage speculation, but it is the fabric of theoretical physics. In
practice there can be benefits, but there can also be unpleasant and
destructive consequence... | 1993-07-01 | 2016-09-06 | [
"math.HO"
] | Arthur Jaffe, Frank Quinn |
math/9301211 | Representations and $K$-theory of Discrete Groups | Let $\Gamma$ be a discrete group of finite virtual cohomological dimension
with certain finiteness conditions of the type satisfied by arithmetic groups.
We define a representation ring for $\Gamma$, determined on its elements of
finite order, which is of finite type. Then we determine the contribution of
this ring to ... | 1993-01-01 | 2009-10-22 | [
"math.KT",
"math.AT"
] | Alejandro Adem |
math/9312212 | The number of independent elements in the product of interval Boolean
algebras | We prove that in the product of kappa many Boolean algebras we cannot find an
independent set of more than 2^kappa elements solving a problem of Monk
(earlier it was known that we cannot find more than 2^{2^kappa} but can find
2^kappa). | 1993-12-15 | 2016-09-06 | [
"math.LO",
"math.GN"
] | Saharon Shelah |
math/9312204 | Strong meager properties for filters | We analyze several ``strong meager'' properties for filters on the natural
numbers between the classical Baire property and a filter being $F_\sigma$. Two
such properties have been studied by Talagrand and a few more combinatorial
ones are investigated. In particular, we define the notion of a P$^+$-filter, a
generaliz... | 1993-12-14 | 2009-09-25 | [
"math.LO"
] | Claude Laflamme |
math/9312203 | Any behaviour of the Mitchell Ordering of Normal Measures Is Possible | Let $U_0,U_1$ be two normal measures on $\kappa .$ We say that $U_0$ is in
the Mitchell ordering less then $U_1,$ $U_0\vartriangleleft U_1,$ if $U_0 \in
Ult(V,U_1) .$ The ordering is well-known to be transitive and well-founded. It
has been an open problem to find a model where the Mitchell ordering embeds the
four-ele... | 1993-12-03 | 2009-09-25 | [
"math.LO"
] | Ji\v{r}\'i Witzany |
math/9311207 | Extensions of the Erd\H{o}s-Rado Theorem | We establish a variety of extensions to the Erdos-Rado Theorem, particularly
involving ordinal numbers, and always involving ordinary partition relations.
Most of the results can be regarded as consequences of the Ramification
Principle, interpreted appropriately. Some of these problems have been open for
a long time. ... | 1993-11-18 | 2009-09-25 | [
"math.LO"
] | J. Baumgartner, A. Hajnal. S. Todorcevic |
math/9311212 | On tree ideals | Let l^0 and m^0 be the ideals associated with Laver and Miller forcing,
respectively. We show that add (l^0) < cov(l^0) and add (m^0) < cov(m^0) are
consistent. We also show that both Laver and Miller forcing collapse the
continuum to a cardinal <= h . | 1993-11-15 | 2008-02-03 | [
"math.LO"
] | Martin Goldstern, Miroslav Repicky, Saharon Shelah, Otmar Spinas |
math/9311211 | Models with second order properties, V: A General principle | We present a general framework for carrying out some constructions. The
unifying factor is a combinatorial principle which we present in terms of a
game in which the first player challenges the second player to carry out
constructions which would be much easier in a generic extension of the
universe, and the second pla... | 1993-11-15 | 2008-02-03 | [
"math.LO"
] | Bradd Hart, Claude Laflamme, Saharon Shelah |
math/9311205 | Applications of cohomology to questions in set theory i: hausdorff gaps | We explore an application of homological algebra to set theoretic objects by
developing a cohomology theory for Hausdorff gaps. The cohomology theory is
introduced with enough generality to be applicable to other questions in set
theory. For gaps, this leads to a natural equivalence notion about which we
answer questio... | 1993-11-15 | 2016-09-06 | [
"math.LO"
] | Daniel Talayco |
math/9311206 | Ultrafilters on omega | A variety of classes of naturally arising ultrafilters on omega is discussed,
and the question is raised whether it is consistent that the classes are empty.
Since all the classes contain the P-point ultrafilters, a negative answer would
greatly extend the famous theorem of Shelah. | 1993-11-15 | 2008-02-03 | [
"math.LO"
] | James E. Baumgartner |
math/9311204 | A combinatorial forcing for coding the universe by a real when there are
no sharps | Assuming 0# does not exist, we present a combinatorial approach to Jensen's
method of coding by a real. The forcing uses combinatorial consequences of fine
structure (including the Covering Lemma, in various guises), but makes no
direct appeal to fine structure itself. | 1993-11-10 | 2009-09-25 | [
"math.LO"
] | Saharon Shelah and Lee Stanley |
math/9311203 | Iterated Class Forcing | In this paper we isolate the notion of Stratified class forcing and show that
Stratification implies cofinality-preservation and is preserved by iterations
with the appropriate support. Many familiar class forcings are stratified and
therefore can be simultaneously iterated without changing cofinalities,
provided the p... | 1993-11-08 | 2008-02-03 | [
"math.LO"
] | Sy D. Friedman (MIT) |
math/9311202 | On hidden extenders | A model with a sequence of indiscernibles depending on a particular
precovering set is constructed.The initial assumption is as follows: for every
n<omega the set {alpha | o(alpha)=alpha^+n } is unbounded in kappa. | 1993-11-04 | 2008-02-03 | [
"math.LO"
] | Moti Gitik |
math/9310213 | IST is more than an algorithm to prove ZFC theorems | There is a sentence in the language of IST, Nelson's internal set theory,
which is not equivalent in IST to a sentence in the ZFC language. Thus the
Reduction algorithm of Nelson, that converts bounded IST formulas with standard
parameters to provably (in IST) equivalent formulas in the ZFC language, cannot
be extended... | 1993-10-26 | 2008-02-03 | [
"math.LO"
] | Vladimir Kanovei |
math/9310224 | Examples for Souslin forcing | We give a model where there is a ccc Souslin forcing which does not satisfy
the Knaster condition. Next, we present a model where there is a sigma-linked
not sigma-centered Souslin forcing such that all its small subsets are
sigma-centered but Martin Axiom fails for this order. Furthermore, we construct
a totally nonho... | 1993-10-15 | 2016-09-06 | [
"math.LO"
] | Haim Judah, Andrzej Ros{\l}anowski, Saharon Shelah |
math/9310212 | How to win some simple iteration games | We introduce two new iteration games: the game G, which is a strengthening of
the weak iteration game, and the game G+, which is somewhat stronger than G but
weaker than the full iteration game of length omega_1.
For a countable M elementarily embeddable in some V_{eta}, we can show that
II wins G(M,omega_1) and that... | 1993-10-09 | 2008-02-03 | [
"math.LO"
] | Alessandro Andretta and John R. Steel |
math/9310211 | Is game semantics necessary? | We discuss the extent to which game semantics is implicit in the formalism of
linear logic and in the intuitions underlying linear logic. | 1993-10-05 | 2008-02-03 | [
"math.LO"
] | Andreas Blass |
math/9310210 | On the divisible parts of quotient groups | Techniques of combinatorial set theory are applied to the following algebraic
problem. Suppose G is an abelian group such that, for all countable subgroups
C, the divisible part of the quotient G/C is countable. What can one conclude
about the size of the divisible part of G/K when the cardinality of the
subgroup K is ... | 1993-10-05 | 2008-02-03 | [
"math.LO"
] | Andreas Blass |
math/9309209 | Possible Behaviours of the Reflection Ordering of Stationary Sets | If $S,T$ are stationary subsets of a regular uncountable cardinal $\kappa$,
we say that $S$ reflects fully in $T$, $S<T$, if for almost all $\alpha \in T$
(except a nonstationary set) $S \cap \alpha$ is stationary in $\alpha .$ This
relation is known to be a well founded partial ordering. We say that a given
poset $P$ ... | 1993-09-16 | 2016-09-06 | [
"math.LO"
] | Ji\v{r}\'i Witzany |
math/9309208 | Questions and answers -- a category arising in linear logic, complexity
theory, and set theory | A category used by de Paiva to model linear logic also occurs in Vojtas's
analysis of cardinal characteristics of the continuum. Its morphisms have been
used in describing reductions between search problems in complexity theory. We
describe this category and how it arises in these various contexts. We also
show how the... | 1993-09-16 | 2009-09-25 | [
"math.LO"
] | Andreas Blass |
math/9309207 | A New Proof of Kunen's Inconsistency | Using elementary pcf, we show that there is no $j:V\to M,$ $M$ transitive,
$j\lambda =\lambda >crit(j),$ $j^{\prime \prime}\lambda \in M.$ | 1993-09-15 | 2008-02-03 | [
"math.LO"
] | Jind\v{r}ich Zapletal |
math/9309204 | Evasion and prediction --- the Specker phenomenon and Gross spaces | We study the set--theoretic combinatorics underlying the following two
algebraic phenomena.
(1) A subgroup G leq Z^omega exhibits the Specker phenomenon iff every
homomorphism G to Z maps almost all unit vectors to 0. Let se be the size of
the smallest G leq Z^omega exhibiting the Specker phenomenon.
(2) Given an u... | 1993-09-09 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle |
math/9309205 | Combinatorial properties of classical forcing notions | We discuss the effect of adding a single real (for various forcing notions
adding reals) on cardinal invariants associated with the continuum (like the
unbounding or the dominating number or the cardinals related to measure and
category on the real line). For random and Cohen forcing, this question was
investigated by ... | 1993-09-09 | 2009-09-25 | [
"math.LO"
] | J\"org Brendle |
math/9309206 | The additivity of porosity ideals | We show that several sigma-ideals related to porous sets have additivity
omega_1 and cofinality 2^omega. This answers a question addressed by Miroslav
Repick'y. | 1993-09-09 | 2009-09-25 | [
"math.LO"
] | J\"org Brendle |
math/9309203 | Ultrafilters: Where topological dynamics = algebra = combinatorics | We survey some connections between topological dynamics, semigroups of
ultrafilters, and combinatorics. As an application, we give a proof, based on
ideas of Bergelson and Hindman, of the Hales-Jewett partition theorem. | 1993-09-08 | 2009-09-25 | [
"math.LO"
] | Andreas Blass |
math/9308203 | The structure of pleasant ideals | Normal ideals on regular uncountable cardinals are familiar objects. We
investigate ideals that are pleasant--while a normal ideal is closed under
arbitrary diagonal unions, a pleasant ideal is closed only under diagonal
unions indexed by sets that are elements of the ideal. We show any selective
ideal extending the no... | 1993-08-24 | 2009-09-25 | [
"math.LO"
] | Christopher Leary |
math/9308202 | Addendum to ``Maximal Chains in $\fomom$ and Ultrapowers of the
Integers'' | Upon presenting the proof of Theorem 3.3 in "Maximal chains in $$ and
ultrapowers of the integers" I discovered that it is not entirely correct and
certainly some details should be added. I have therefore written an addendum to
the paper and made it available by ftp. Unfortunately the published version
will be somewhat... | 1993-08-20 | 2008-02-03 | [
"math.LO"
] | Saharon Shelah, Juris Stepr\=ans |
math/9308221 | Universal graphs without large cliques | We give some existence/nonexistence statements on universal graphs, which
under GCH give a necessary and sufficient condition for the existence of a
universal graph of size lambda with no K(kappa), namely, if either kappa is
finite or cf(kappa)>cf(lambda). (Here K(kappa) denotes the complete graph on
kappa vertices.) T... | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Peter Komjath, Saharon Shelah |
math/9308210 | The canary tree | A canary tree is a tree of cardinality the continuum which has no uncountable
branch, but gains a branch whenever a stationary set is destroyed (without
adding reals). Canary trees are important in infinitary model theory. The
existence of a canary tree is independent of ZFC + GCH. | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Alan H. Mekler, Saharon Shelah |
math/9308215 | Dominating functions and graphs | A graph is called dominating if its vertices can be labelled with integers in
such a way that for every function f: omega-> omega the graph contains a ray
whose sequence of labels eventually exceeds f. We obtain a characterization of
these graphs by producing a small family of dominating graphs with the property
that e... | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Reinhard Diestel, Saharon Shelah, Juris Stepr\=ans |
math/9308212 | On CH + 2^{aleph_1}-> (alpha)^2_2 for alpha < omega_2 | We prove the consistency of ``CH + 2^{aleph_1} is arbitrarily large +
2^{aleph_1} not-> (omega_1 x omega)^2_2''. If fact, we can get 2^{aleph_1}
not-> [omega_1 x omega]^2_{aleph_0}. In addition to this theorem, we give
generalizations to other cardinals. | 1993-08-15 | 2009-09-25 | [
"math.LO"
] | Saharon Shelah |
math/9308216 | A saturated model of an unsuperstable theory of cardinality greater than
its theory has the small index property | A model M of cardinality lambda is said to have the small index property if
for every G subseteq Aut(M) such that [Aut(M):G] <= lambda there is an A
subseteq M with |A|< lambda such that Aut_A(M) subseteq G. We show that if M^*
is a saturated model of an unsuperstable theory of cardinality > Th(M), then
M^* has the sma... | 1993-08-15 | 2009-09-25 | [
"math.LO"
] | Garvin Melles, Saharon Shelah |
math/9308211 | On a conjecture regarding nonstandard uniserial modules | We consider the question of which valuation domains (of cardinality aleph_1)
have non-standard uniserial modules. We show that a criterion conjectured by
Osofsky is independent of ZFC + GCH. | 1993-08-15 | 2008-02-03 | [
"math.LO",
"math.RA"
] | Paul C. Eklof, Saharon Shelah |
math/9308214 | Somewhere trivial automorphisms | It is shown to be consistent that there is a non-trivial autohomeomorphism of
beta N while all such autohomeomorphisms are trivial on some open set. The
model used is one due to Velickovic in which, coincidentally, Martin's Axiom
also holds. | 1993-08-15 | 2016-09-06 | [
"math.LO",
"math.GN"
] | Saharon Shelah, Juris Stepr\=ans |
math/9308219 | Peano Arithmetic may not be interpretable in the monadic theory of
orders | Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in
the monadic second-order theory of short chains (hence, in the monadic
second-order theory of the real line). We show here that it is consistent that
there is no interpretation even in the monadic second-order theory of all
chains. | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Shmuel Lifsches, Saharon Shelah |
math/9308213 | On coherent systems of projections for aleph_1 separable groups | It is proved consistent with either CH or the negation of CH that there is an
aleph_1-separable group of cardinality aleph_1 which does not have a coherent
system of projections. It had previously been shown that it is consistent with
not CH that every aleph_1-separable group of cardinality aleph_1 does have a
coherent... | 1993-08-15 | 2016-09-06 | [
"math.LO",
"math.RA"
] | Paul C. Eklof, Alan H. Mekler, Saharon Shelah |
math/9308220 | Consequences of arithmetic for set theory | In this paper, we consider certain cardinals in ZF (set theory without AC,
the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D,
either C <= D or D <= C. However, in ZF this is no longer so. For a given
infinite set A consider Seq(A), the set of all sequences of A without
repetition. We compar... | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Lorenz Halbeisen, Saharon Shelah |
math/9308217 | Number of open sets for a topology with a countable basis | Let T be the family of open subsets of a topological space (not necessarily
Hausdorff or even T_0). We prove that if T has a countable base and is not
countable, then T has cardinality at least continuum. | 1993-08-15 | 2008-02-03 | [
"math.LO",
"math.GN"
] | Saharon Shelah |
math/9308218 | A model in which there are Jech-Kunen trees but there are no Kurepa
trees | By an omega_1 --tree we mean a tree of power omega_1 and height omega_1. We
call an omega_1 --tree a Jech--Kunen tree if it has kappa --many branches for
some kappa strictly between omega_1 and 2^{omega_1}. In this paper we construct
the models of CH plus 2^{omega_1}> omega_2, in which there are Jech--Kunen
trees and t... | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Renling Jin, Saharon Shelah |
math/9308222 | On uniformly antisymmetric functions | We show that there is always a uniformly antisymmetric f:A-> {0,1} if A
subset R is countable. We prove that the continuum hypothesis is equivalent to
the statement that there is an f:R-> omega with |S_x| <= 1 for every x in R. If
the continuum is at least aleph_n then there exists a point x such that S_x has
at least ... | 1993-08-15 | 2016-09-06 | [
"math.LO"
] | Peter Komjath, Saharon Shelah |
math/9308201 | An application of Shoenfield's absoluteness theorem to the theory of
uniform distribution | If (B_x: x in N) is a Borel family of sets, indexed by the Baire space N =
omega^omega, all B_x have measure zero, and the family is increasing, then the
union of all B_x also has measure zero. We give two proofs of this theorem: one
in the language of set theory, using Shoenfield's theorem on Sigma-1-2 sets,
the other... | 1993-08-06 | 2008-02-03 | [
"math.LO"
] | Martin Goldstern |
math/9306214 | Strong measure zero sets without Cohen reals | If ZFC is consistent, then each of the following are consistent with ZFC +
2^{{aleph_0}}= aleph_2 :
1.) X subseteq R is of strong measure zero iff |X| <= aleph_1 + there is a
generalized Sierpinski set.
2.) The union of aleph_1 many strong measure zero sets is a strong measure
zero set + there is a strong measure z... | 1993-06-15 | 2009-09-25 | [
"math.LO"
] | Martin Goldstern, Haim Judah, Saharon Shelah |
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