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 |
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math/9212206 | Sur les op\'erateurs factorisables par $OH$ | Let $H,K$ be Hilbert spaces. Let $E \subset B(H)$ and $F \subset B(K)$ be
operator spaces in the sense of [1,2]. We study the operators $u : E \to F$
which admit a factorization $E \to OH \to F$ with completely bounded maps
through the operator Hilbert space $OH$ which we have introduced and studied in
a recent note. W... | 1992-12-04 | 2016-09-06 | [
"math.FA"
] | Gilles Pisier |
math/9212205 | On the ``local theory'' of operator spaces | In Banach space theory, the ``local theory'' refers to the collection of
finite dimensional methods and ideas which are used to study infinite
dimensional spaces (see e.g. [P4,TJ]). It is natural to try to develop an
analogous theory in the recently developed category of operator spaces
[BP,B1-2,BS,ER1-7,Ru]. The objec... | 1992-12-04 | 2009-09-25 | [
"math.FA"
] | Gilles Pisier |
math/9212204 | Interpolation Between $H^p$ Spaces and Non-Commutative Generalizations
II | We continue an investigation started in a preceding paper. We discuss the
classical results of Carleson connecting Carleson measures with the
$\d$-equation in a slightly more abstract framework than usual. We also
consider a more recent result of Peter Jones which shows the existence of a
solution of the $\d$-equation,... | 1992-12-04 | 2016-09-06 | [
"math.FA"
] | Gilles Pisier |
math/9211212 | Infinite order decoupling of random chaoses in Banach space | We prove a number of decoupling inequalities for nonhomogeneous random
polynomials with coefficients in Banach space. Degrees of homogeneous
components enter into comparison as exponents of multipliers of terms of
certain Poincar\'e-type polynomials. It turns out that the fulfillment of most
of types of decoupling ineq... | 1992-11-18 | 2016-09-06 | [
"math.FA"
] | Jerzy Szulga |
math/9211210 | Polynomial Schur and Polynomial Dunford-Pettis Properties | A Banach space is {\it polynomially Schur} if sequential convergence against
analytic polynomials implies norm convergence. Carne, Cole and Gamelin show
that a space has this property and the Dunford-Pettis property if and only if
it is Schur. Herein is defined a reasonable generalization of the
Dunford--Pettis propert... | 1992-11-17 | 2016-09-06 | [
"math.FA"
] | Jeff Farmer, William B. Johnson |
math/9211211 | Norms of Minimal Projections | It is proved that the projection constants of two- and three-dimensional
spaces are bounded by $4/3$ and $(1+\sqrt 5)/2$, respectively. These bounds are
attained precisely by the spaces whose unit balls are the regular hexagon and
dodecahedron. In fact, a general inequality for the projection constant of a
real or comp... | 1992-11-17 | 2016-09-06 | [
"math.FA"
] | Hermann K\"onig, Nicole Tomczak-Jaegermann |
math/9211209 | Common subspaces of $L_{p}$-spaces | For $n\geq 2, p<2$ and $q>2,$ does there exist an $n$-dimensional Banach
space different from Hilbert spaces which is isometric to subspaces of both
$L_{p}$ and $L_{q}$? Generalizing the construction from the paper "Zonoids
whose polars are zonoids" by R.Schneider we give examples of such spaces.
Moreover, for any comp... | 1992-11-05 | 2009-09-25 | [
"math.FA"
] | Alexander Koldobsky |
math/9211208 | Surjective isometries on rearrangement-invariant spaces | We prove that if $X$ is a real rearrangement-invariant function space on
$[0,1]$, which is not isometrically isomorphic to $L_2,$ then every surjective
isometry $T:X\to X$ is of the form $Tf(s)=a(s)f(\sigma(s))$ for a Borel
function $a$ and an invertible Borel map $\sigma:[0,1] \to [0,1].$ If $X$ is
not equal to $L_p$,... | 1992-11-05 | 2009-09-25 | [
"math.FA"
] | Nigel J. Kalton, Beata Randrianantoanina |
math/9211207 | Factorization theorems for quasi-normed spaces | We extend Pisier's abstract version of Grothendieck's theorem to general
non-locally convex quasi-Banach spaces. We also prove a related result on
factoring operators through a Banach space and apply our results to the study
of vector-valued inequalities for Sidon sets. We also develop the local theory
of (non-locally ... | 1992-11-02 | 2008-02-03 | [
"math.FA"
] | Nigel J. Kalton, Sik-Chung Tam |
math/9210209 | Two Remarks on Marcinkiewicz decompositions by Holomorphic Martingales | The real part of $H^\infty(\bT)$ is not dense in $L^\infty_{\tR}(\bT)$. The
John-Nirenberg theorem in combination with the Helson-Szeg\"o theorem and the
Hunt Muckenhaupt Wheeden theorem has been used to determine whether $f\in
L^\infty_{\tR}(\bT)$ can be approximated by $\Re H^\infty(\bT)$ or not:
$\dist(f,\Re H^\inft... | 1992-10-30 | 2016-09-06 | [
"math.FA"
] | Paul F. X. M\"uller |
math/9210211 | Unrestricted products of contractions in Banach spaces | Let $X$ be a reflexive Banach space such that for any $x \ne 0$ the set $$
\{x^* \in X^*: \text {$\|x^*\|=1$ and $x^*(x)=\|x\|$}\} $$ is compact. We prove
that any unrestricted product of of a finite number of $(W)$ contractions on
$X$ converges weakly. | 1992-10-30 | 2016-09-06 | [
"math.FA"
] | P. K. Lin |
math/9210208 | Mean Convergence of Vector--valued Walsh Series | Given any Banach space $X$, let $L_2^X$ denote the Banach space of all
measurable functions $f:[0,1]\to X$ for which
||f||_2:=(int_0^1 ||f(t)||^2 dt)^{1/2}
is finite. We show that $X$ is a UMD--space (see \cite{BUR:1986}) if and only
if
\lim_n||f-S_n(f)||_2=0 for all $f\in L_2^X$, where
S_n(f):=sum_{i=0}^{n-1} ... | 1992-10-30 | 2016-09-06 | [
"math.FA"
] | Joerg Wenzel |
math/9210210 | Weakly Lindelof determined Banach spaces not containing $\ell^1(N)$ | The class of countably intersected families of sets is defined. For any such
family we define a Banach space not containing $\ell^{1}(\NN )$. Thus we obtain
counterexamples to certain questions related to the heredity problem for W.C.G.
Banach spaces. Among them we give a subspace of a W.C.G. Banach space not
containin... | 1992-10-30 | 2016-09-06 | [
"math.FA"
] | Spiros A. Argyros |
math/9210207 | Schoenberg's Problem on Positive Definite Functions | If $n \ge 3$, $q>2$ and $\beta > 0$ then the function
$\exp(-(|x_1|^q+|x_2|^q+\dots+|x_n|^q)^{\beta/q})$\ is not positive definite.
This result gives an answer to a question posed by I.J.~Schoenberg in 1938.
This text is an authorized English translation of the paper published in
Russian in Algebra and Analysis 3(1991)... | 1992-10-19 | 2008-02-03 | [
"math.FA"
] | Alexander Koldobsky |
math/9210206 | Interpolation of compact operators by the methods of Calder\'on and
Gustavsson-Peetre | Let $ X=(X_0,X_1)$ and $ Y=(Y_0,Y_1)$ be Banach couples and suppose $T: X\to
Y$ is a linear operator such that $T:X_0\to Y_0$ is compact. We consider the
question whether the operator $T:[X_0,X_1]_{\theta}\to [Y_0,Y_1]_{\theta}$ is
compact and show a positive answer under a variety of conditions. For example
it suffice... | 1992-10-08 | 2016-09-06 | [
"math.FA"
] | Michael Cwikel, Nigel J. Kalton |
math/9210205 | A characterization of Banach spaces containing $c_0$ | A subsequence principle is obtained, characterizing Banach spaces containing
$c_0$, in the spirit of the author's 1974 characterization of Banach spaces
containing $\ell^1$.
Definition: A sequence $(b_j)$ in a Banach space is called {\it strongly
summing\/} (s.s.) if $(b_j)$ is a weak-Cauchy basic sequence so that wh... | 1992-10-08 | 2016-09-06 | [
"math.FA"
] | Haskell P. Rosenthal |
math/9210220 | Prevalence: a translation-invariant ``almost every'' on
infinite-dimensional spaces | We present a measure-theoretic condition for a property to hold ``almost
everywhere'' on an infinite-dimensional vector space, with particular emphasis
on function spaces such as $C^k$ and $L^p$. Like the concept of ``Lebesgue
almost every'' on finite-dimensional spaces, our notion of ``prevalence'' is
translation inva... | 1992-10-01 | 2016-09-06 | [
"math.FA",
"math.DS"
] | Brian R. Hunt |
math/9209217 | Calder\'on couples of re-arrangement invariant spaces | We examine conditions under which a pair of re-arrangement invariant function
spaces on $[0,1]$ or $[0,\infty)$ form a Calder\'on couple. A very general
criterion is developed to determine whether such a pair is a Calder\'on couple,
with numerous applications. We give, for example, a complete classification of
those sp... | 1992-09-25 | 2016-09-06 | [
"math.FA"
] | Nigel J. Kalton |
math/9209216 | On vector-valued inequalities for Sidon sets and sets of interpolation | Let $E$ be a Sidon subset of the integers and suppose $X$ is a Banach space.
Then Pisier has shown that $E$-spectral polynomials with values in $X$ behave
like Rademacher sums with respect to $L_p-$norms. We consider the situation
when $X$ is a quasi-Banach space. For general quasi-Banach spaces we show that
a similar ... | 1992-09-25 | 2009-09-25 | [
"math.FA"
] | Nigel J. Kalton |
math/9209215 | Computing p-summing norms with few vectors | It is shown that the p-summing norm of any operator with n-dimensional domain
can be well-aproximated using only ``few" vectors in the definition of the
p-summing norm. Except for constants independent of n and log n factors, ``few"
means n if 1<p<2 and n^{p/2} if 2<p<infinity. | 1992-09-22 | 2016-09-06 | [
"math.FA"
] | William B. Johnson, Gideon Schechtman |
math/9209214 | Asymptotic $l_p$ spaces and bounded distortions | The new class of Banach spaces, so-called asymptotic $l_p$ spaces, is
introduced and it is shown that every Banach space with bounded distortions
contains a subspace from this class.
The proof is based on an investigation of certain functions, called
enveloping functions, which are intimately connected with stabiliza... | 1992-09-15 | 2009-09-25 | [
"math.FA"
] | Vitali D. Milman, Nicole Tomczak-Jaegermann |
math/9209213 | The theorems of Caratheodory and Gluskin for $0<p<1$ | In this note we investigate some aspects of the local structure of finite
dimensional $p$-Banach spaces. The well known theorem of Gluskin gives a sharp
lower bound of the diameter of the Minkowski compactum. In [Gl] it is proved
that diam$({\cal M}_n^1)\geq cn$ for some absolute constant $c$. Our purpose is
to study t... | 1992-09-10 | 2016-09-06 | [
"math.FA"
] | Jesus Bastero, J. Buernes, A. Pena |
math/9209211 | Amenability of Banach algebras of compact operators | In this paper we study conditions on a Banach space X that ensure that the
Banach algebra K(X) of compact operators is amenable. We give a symmetrized
approximation property of X which is proved to be such a condition. This
property is satisfied by a wide range of Banach spaces including all the
classical spaces. We th... | 1992-09-08 | 2008-02-03 | [
"math.FA"
] | Niels Gronbaek, Barry E. Johnson, George A. Willis |
math/9209212 | The Distribution of Non-Commutative Rademacher Series | We give a formula for the tail of the distribution of the non-commutative
Rademacher series, which generalizes the result that is already available in
the commutative case. As a result, we are able to calculate the norm of these
series in many rearrangement invariant spaces, generalizing work of Pisier and
Rodin and Se... | 1992-09-08 | 2008-02-03 | [
"math.FA"
] | Stephen J. Montgomery-Smith |
math/9208202 | Vector-valued Lagrange interpolation and mean convergence of Hermite
series | Let X be a Banach space and $1\le p<\infty$. We prove interpolation
inequalities of Marcinkiewicz-Zygmund type for X-valued polynomials g of degree
$\le n$ on $R$,
\[c_p (\sum\limits_{i=1}^{n+1} \mu_i \| g(t_i)e^{-t_i^2 /2} \|^p)^{1/p} \le
(\int\limits_{\RR}^{} \|g(t)e^{-t^2 /2} \|^p dt)^{1/p} \le d_p
(\sum\limits_{i... | 1992-08-13 | 2016-09-06 | [
"math.FA"
] | Hermann K\"onig |
math/9208201 | Vector-valued L_p convergence of orthogonal series and Lagrange
interpolation | We give necessary and sufficient conditions for interpolation inequalities of
the type considered by Marcinkiewicz and Zygmund to be true in the case of
Banach space-valued polynomials and Jacobi weights and nodes. We also study the
vector-valued expansion problem of $L_p$-functions in terms of Jacobi
polynomials and c... | 1992-08-13 | 2016-09-06 | [
"math.FA"
] | Hermann K\"onig and Niels J. Nielsen |
math/9207208 | On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices | We prove that if X is an infinite dimensional Banach lattice with a weak unit
then there exists a probability space (Omega, Sigma,mu) so that the unit sphere
S(L_1(Omega, Sigma, mu) is uniformly homeomorphic to the unit sphere S(X) if
and only if X does not contain l_{infty}^n's uniformly. | 1992-07-21 | 2016-09-06 | [
"math.FA"
] | Fouad Chaatit |
math/9207207 | On Weakly Null FDD's in Banach Spaces | In this paper we show that every sequence (F_n) of finite dimensional
subspaces of a real or complex Banach space with increasing dimensions can be
``refined'' to yield an F.D.D. (G_n), still having increasing dimensions, so
that either every bounded sequence (x_n), with x_n in G_n for n in N, is weakly
null, or every ... | 1992-07-21 | 2016-09-06 | [
"math.FA"
] | Edward Odell, Haskell P. Rosenthal, Thomas Schlumprecht |
math/9207206 | Banach Spaces Of The Type Of Tsirelson | To any pair ( M , theta ) where M is a family of finite subsets of N compact
in the pointwise topology, and 0<theta < 1 , we associate a Tsirelson-type
Banach space T_M^theta . It is shown that if the Cantor-Bendixson index of M is
greater than n and theta >{1/n} then T_M^theta is reflexive. Moreover, if the
Cantor-Ben... | 1992-07-06 | 2016-09-06 | [
"math.FA"
] | Spiros A. Argyros, Irene Deliyanni |
math/9206202 | On nonatomic Banach lattices and Hardy spaces | We are interested in the question when a Banach space $X$ with an
unconditional basis is isomorphic (as a Banach space) to an order-continuous
nonatomic Banach lattice. We show that this is the case if and only if $X$ is
isomorphic as a Banach space with $X(\ell_2)$. This and results of J. Bourgain
are used to show tha... | 1992-06-05 | 2008-02-03 | [
"math.FA"
] | Nigel J. Kalton, P. Wojtaszczyk |
math/9206204 | More smoothly real compact spaces | A topological space $X$ is called $\Cal A$-real compact, if every algebra
homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$,
where $\Cal A$ is an algebra of continuous functions. Our main interest lies on
algebras of smooth functions. In \cite{AdR} it was shown that any separable
Banach spac... | 1992-06-01 | 2016-09-06 | [
"math.FA"
] | Andreas Kriegl, Peter W. Michor |
math/9206201 | The distribution of vector-valued Rademacher series | Let $X=\sum \epsilon_n x_n$ be a Rademacher series with vector-valued
coefficients. We obtain an approximate formula for the distribution of the
random variable $||X||$ in terms of its mean and a certain quantity derived
from the K-functional of interpolation theory. Several applications of the
formula are given. | 1992-06-01 | 2008-02-03 | [
"math.FA"
] | Stephen J. Dilworth, Stephen J. Montgomery-Smith |
math/9205207 | Some Questions Arising from the Homogeneous Banach Space Problem | We review the current state of the homogeneous Banach space problem. We then
formulate several questions which arise naturally from this problem, some of
which seem to be fundamental but new. We give many examples defining the bounds
on the problem. We end with a simple construction showing that every infinite
dimensio... | 1992-05-21 | 2016-09-06 | [
"math.FA"
] | Peter G. Casazza |
math/9205206 | Set-functions and factorization | If $\phi$ is a submeasure satisfying an appropriate lower estimate we give a
quantitative result on the total mass of a measure $\mu$ satisfying
$0\le\mu\le\phi.$ We give a dual result for supermeasures and then use these
results to investigate convexity on non-locally convex quasi-Banach lattices.
We then show how to ... | 1992-05-11 | 2008-02-03 | [
"math.FA"
] | Nigel J. Kalton, Stephen J. Montgomery-Smith |
math/9205205 | On $c_0$-saturated Banach spaces | A Banach space E is c_0-saturated if every closed infinite dimensional
subspace of E contains an isomorph of c_0. A c_0-saturated Banach space with an
unconditional basis which has a quotient space isomorphic to l^2 is
constructed. | 1992-05-07 | 2016-09-06 | [
"math.FA"
] | Denny H. Leung |
math/9205204 | The unconditional basic sequence problem | We construct a Banach space that does not contain any infinite unconditional
basic sequence. | 1992-05-06 | 2009-09-25 | [
"math.FA"
] | W. T. Gowers, Bernard Maurey |
math/9205203 | The Compact Approximation Property does not imply the Approximation
Property | It is shown how to construct, given a Banach space which does not have the
approximation property, another Banach space which does not have the
approximation property but which does have the compact approximation property. | 1992-05-04 | 2009-09-25 | [
"math.FA"
] | George A. Willis |
math/9204215 | A l_1-predual which is not isometric to a quotient of C(alpha) | About twenty years ago Johnson and Zippin showed that every separable
L_1(mu)-predual was isometric to a quotient of C(Delta ), where Delta is the
Cantor set. In this note we will show that the natural analogue of the theorem
for l_1-preduals does not hold. We will show that there are many l_1-preduals
which are not is... | 1992-04-27 | 2016-09-06 | [
"math.FA"
] | Dale E. Alspach |
math/9204216 | Jean Bourgain's analytic partition of unity via holomorphic martingales | Using stopping time arguments on holomorphic martingales we present a soft
way of constructing J. Bourgain's analytic partitions of unity. Applications to
Marcinkiewicz interploation in weighted Hardy spaces are discussed. | 1992-04-27 | 2016-09-06 | [
"math.FA"
] | Paul F. X. M\"uller |
math/9204214 | A Note on Unconditional Structures in Weak Hilbert Spaces | We prove that if a non-atomic separable Banach lattice in a weak Hilbert
space, then it is lattice isomorphic to $L_2(0,1)$. | 1992-04-24 | 2008-02-03 | [
"math.FA"
] | Niels Jorgen Nielsen |
math/9204213 | The Distorion Problem | We prove that Hilbert space is distortable and, in fact, arbitrarily
distortable. This means that for all lambda >1 there exists an equivalent norm
|.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there
exist x,y in Y with ||x||_2 = ||y||_2 =1 yet |x| >lambda |y|.
We also prove that if X is any in... | 1992-04-21 | 2016-09-06 | [
"math.FA"
] | Edward Odell, Thomas Schlumprecht |
math/9204212 | The volume of the intersection of a convex body with its translates | It is proved that for a symmetric convex body K in R^n, if for some tau > 0,
|K cap (x+tau K)| depends on ||x||_K only, then K is an ellipsoid. As a part of
the proof, smoothness properties of convolution bodies ls are studied. | 1992-04-14 | 2016-09-06 | [
"math.FA"
] | Mathieu Meyer, Shlomo Reisner, M. Schmuckenschlager |
math/9204211 | Structure of local Banach spaces of locally convex spaces | We show that a continuous bilinear mapping P: C(I) \times C(I) \to C(I) can
be presented in the form P(f,g) = B((Af)(Ag)), where A and B are bounded linear
operators on C(I) and multiplication is defined pointwise, if and only if for
all t in I the bilinear form (f,g) -> P(f,g)(t) is integral on C(I) times C(I)
and dep... | 1992-04-01 | 2016-09-06 | [
"math.FA"
] | Jari Taskinen |
math/9202203 | Lower estimates of random unconditional constants of Walsh-Paley
martingales with values in banach spaces | For a Banach space X we define RUMD_n(X) to be the infimum of all c>0 such
that (AVE_{\epsilon_k =\pm 1} || \sum_1^n epsilon_k (M_k - M_{k-1}
)||_{L_2^X}^2 )^{1/2} <= c || M_n ||_{L_2^X} holds for all Walsh-Paley
martingales {M_k}_0^n subset L_2^X with M_0 =0. We relate the asymptotic
behaviour of the sequence {RUMD(X)... | 1992-02-28 | 2008-02-03 | [
"math.FA"
] | Stefan Geiss |
math/9202204 | Complexity of weakly null sequences | We introduce an ordinal index which measures the complexity of a weakly null
sequence, and show that a construction due to J. Schreier can be iterated to
produce for each alpha < omega_1, a weakly null sequence (x^{alpha}_n)_n in
C(omega^{omega^{alpha}})) with complexity alpha. As in the Schreier example
each of these ... | 1992-02-28 | 2009-09-25 | [
"math.FA"
] | Dale E. Alspach and Spiros Argyros |
math/9202202 | On the integration of vector-valued functions | We discuss relationships between the McShane, Pettis, Talagrand and Bochner
integrals. A large number of different methods of integration of
Banach-space-valued functions have been introduced, based on the various
possible constructions of the Lebesgue integral. They commonly run fairly
closely together when the range ... | 1992-02-21 | 2016-09-06 | [
"math.FA"
] | D. H. Fremlin, Jose Mendoza |
math/9201237 | Isomorphisms of certain weak L^p spaces | It is shown that the weak $L^p$ spaces $\ell^{p,\infty}, L^{p,\infty}[0,1]$,
and $L^{p,\infty}[0,\infty)$ are isomorphic as Banach spaces. | 1992-01-14 | 2009-09-25 | [
"math.FA"
] | Denny H. Leung |
math/9201202 | Factorizations of natural embeddings of l_p^n int L_r | This is a continuation of the paper [FJS] with a similar title. Several
results from there are strengthened, in particular:
1. If T is a "natural" embedding of l_2^n into L_1 then, for any well-bounded
factorization of T through an L_1 space in the form T=uv with v of norm one, u
well-preserves a copy of l_1^k with k... | 1992-01-06 | 2009-09-25 | [
"math.FA"
] | Tadek Figiel, William B. Johnson, and Gideon Schechtman |
math/9201254 | A convenient setting for real analytic mappings | We present here "the" cartesian closed theory for real analytic mappings. It
is based on the concept of real analytic curves in locally convex vector
spaces. A mapping is real analytic, if it maps smooth curves to smooth curves
and real analytic curves to real analytic curves. Under mild completeness
conditions the sec... | 1992-01-01 | 2016-09-06 | [
"math.FA",
"math.CA",
"math.DG"
] | Andreas Kriegl, Peter W. Michor |
math/9210221 | On the Burnside problem on periodic groups | It is proved that the free $m$-generated Burnside groups $\Bbb{B}(m,n)$ of
exponent $n$ are infinite provided that $m>1$, $n\ge2^{48}$. | 1992-10-01 | 2009-09-25 | [
"math.GR"
] | Sergei V. Ivanov |
math/9210219 | The 1-, 2-, and 3-characters determine a group | A set of invariants for a finite group is described. These arise naturally
from Frobenius' early work on the group determinant and provide an answer to a
question of Brauer. Whereas it is well known that the ordinary character table
of a group does not determine the group uniquely, it is a consequence of the
results pr... | 1992-10-01 | 2008-02-03 | [
"math.GR"
] | Hans-J\"urgen Hoehnke, Kenneth W. Johnson |
math/9204220 | Knit products of graded Lie algebras and groups | If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its
bracket can be written in a form that mimics a "double sided semidirect
product". It is called the {\it knit product} of the two subalgebras then. The
integrated version of this is called a {\it knit product} of groups --- it
coincides with t... | 1992-04-01 | 2016-09-06 | [
"math.GR",
"math.RA"
] | Peter W. Michor |
math/9201264 | Semistability of amalgamated products, HNN-extensions, and all
one-relator groups | The authors announce the following theorem.
Theorem 1. If $G=A*_H B$ is an amalgamated product where $A$ and $B$ are
finitely presented and semistable at infinity, and $H$ is finitely generated,
then $G$ is semistable at infinity. If $G=A*_H$ is an HNN-extension where $A$
is finitely presented and semistable at infin... | 1992-01-01 | 2008-02-03 | [
"math.GR",
"math.GT"
] | Michael L. Mihalik, Steven T. Tschantz |
math/9201265 | $\Lambda$\<-Trees and Their Applications | To most mathematicians and computer scientists the word ``tree'' conjures up,
in addition to the usual image, the image of a connected graph with no
circuits. In the last few years various types of trees have been the subject of
much investigation, but this activity has not been exposed much to the wider
mathematical c... | 1992-01-01 | 2016-09-06 | [
"math.GR",
"math.DS",
"math.GT"
] | John W. Morgan |
math/9210224 | Riemann surfaces and the geometrization of 3-manifolds | About a decade ago Thurston proved that a vast collection of 3-manifolds
carry metrics of constant negative curvature. These manifolds are thus elements
of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a
closed manifold, Mostow rigidity assures that a hyperbolic structure is unique
when it ex... | 1992-10-01 | 2016-09-06 | [
"math.GT",
"math.CV"
] | Curt McMullen |
math/9201263 | Pleating coordinates for the Teichm\"{u}ller space of a punctured torus | We construct new coordinates for the Teichm\"uller space Teich of a punctured
torus into $\bold{R} \times\bold{R}^+$. The coordinates depend on the
representation of Teich as a space of marked Kleinian groups $G_\mu$ that
depend holomorphically on a parameter $\mu$ varying in a simply connected
domain in $\bold{C}$. Th... | 1992-01-01 | 2016-09-06 | [
"math.GT",
"math.CV"
] | Linda Keen, Caroline Series |
math/9205211 | Two notes on notation | The author advocates two specific mathematical notations from his popular
course and joint textbook, "Concrete Mathematics". The first of these,
extending an idea of Iverson, is the notation "[P]" for the function which is 1
when the Boolean condition P is true and 0 otherwise. This notation can
encourage and clarify t... | 1992-05-01 | 2008-02-03 | [
"math.HO"
] | Donald E. Knuth |
math/9201262 | Editors' remarks (on two complexity theory surveys in the Bulletin) | The authors discuss the role of controversy in mathematics as a preface to
two opposing articles on computational complexity theory: "Some basic
information on information-based complexity theory" by Beresford Parlett
[math.NA/9201266] and "Perspectives on information-based complexity" by J. F.
Traub and Henryk Wo\'zni... | 1992-01-01 | 2008-02-03 | [
"math.HO"
] | Morris W. Hirsch, Richard S. Palais |
math/9212202 | A large Pi-1-2 set absolute for set forcing | Let k be a definable L-cardinal. Then there is a set of reals X,
class-generic over L, such that L(X) and L have the same cardinals, X has size
k in L(X) and some pi-1-2 formula defines X in all set-generic extensions of
L(X). Two corollaries, both assuming the consistency of an inaccessible: It is
consistent for the P... | 1992-12-02 | 2009-09-25 | [
"math.LO"
] | Sy D. Friedman (MIT) |
math/9212201 | Jensen's \Sigma^* theory and the combinatorial content of V=L | The purpose of this article is to indicate how a reformulation of Jensen's
$\Sigma^*$ theory (developed for the study of core models) can be used to
provide a more satisfactory treatment of uniformization, hulls and Skolem
functions for the $J_\alpha$'s. Then we use this approach to fine structure to
formulate a princi... | 1992-12-02 | 2008-02-03 | [
"math.LO"
] | Sy D. Friedman (MIT) |
math/9211206 | Measurable rectangles | We give an example of a measurable set of reals E such that the set
E'={(x,y): x+y in E} is not in the sigma-algebra generated by the rectangles
with measurable sides. We also prove a stronger result that there exists an
analytic set E such that E' is not in the sigma-algebra generated by rectangles
whose horizontal si... | 1992-11-25 | 2008-02-03 | [
"math.LO"
] | Arnold W. Miller |
math/9211204 | A simpler proof of Jensen's coding theorem | We present a simplification of Jensen's proof of his Coding Theorem (even in
the case where 0# exists). The proof avoids Jensen's split into cases according
to whether or not 0# exists.
In addition, the paper contains self-contained proofs of the necessary forms
of Square and Diamond, based on an approach to fine str... | 1992-11-24 | 2009-09-25 | [
"math.LO"
] | Sy D. Friedman (MIT) |
math/9211205 | Minimal universes | An inner model M is MINIMAL if there is a class A such that <M,A> is amenable
yet has no transitive proper elementary submodel. We study minimal universes in
the context of 0#. For example we prove: If 0# exists then there is an inner
model which is minimal and locally generic over L(i.e., every set in the inner
model ... | 1992-11-24 | 2008-02-03 | [
"math.LO"
] | Sy D. Friedman (MIT) |
math/9211203 | The Genericity Conjecture | In this paper we produce a real r such that 0<r<0# in L-degree, yet R is NOT
generic over L (for a forcing amenable to L). This answers a question of
Beller-Jensen-Welch. | 1992-11-24 | 2008-02-03 | [
"math.LO"
] | Sy D. Friedman (MIT) |
math/9211214 | Planting Kurepa trees and killing Jech-Kunen trees in a model by using
one inaccessible cardinal | By an omega_1--tree we mean a tree of power omega_1 and height omega_1. Under
CH and 2^{omega_1}> omega_2 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 prove that, assuming the existence of one
inaccessible cardinal,
... | 1992-11-15 | 2016-09-06 | [
"math.LO"
] | Renling Jin, Saharon Shelah |
math/9211213 | Baire property and Axiom of Choice | We show that
(1) If ZF is consistent then the following theory is consistent "ZF +
DC(omega_{1}) + Every set of reals has Baire property" and
(2) If ZF is consistent then the following theory is consistent "ZFC + `every
projective set of reals has Baire property' + `any union of omega_{1} meager
sets is meager' ". | 1992-11-15 | 2019-08-27 | [
"math.LO"
] | Haim Judah, Saharon Shelah |
math/9211202 | Combinatorial properties of Hechler forcing | In this work we use a notion of rank first introduced by James Baumgartner
and Peter Dordal and later developed independently by the third author to show
that adding a Hechler real has strong combinatorial consequences.
We prove:
1) assuming omega_1^V = omega_1^L, there is no real in V[d] which is
eventually differ... | 1992-11-03 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle, Haim Judah and Saharon Shelah |
math/9211201 | Set-theoretic aspects of periodic $FC$-groups --- extraspecial p-groups
and Kurepa trees | Given a group G, we let Z(G) denote its center, G' its commutator subgroup,
and Phi (G) its Frattini subgroup (the intersection of all maximal proper
subgroups of G). Given U leq G, we let N_G (U) stand for the normalizer of U in
G. A group G is FC iff every element g in G has finitely many conjugates. A
p-group E is c... | 1992-11-03 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle |
math/9210204 | Splitting number and the core model | We can generalize the definition of {\it splitting number } $s(\kappa )$ for
$\kappa$ uncountable regular: $s(\kappa )=min\{ |\Cal S|:\Cal S\subset \Cal
P(\kappa ) \forall a\in \kappa ^\kappa \exists b\in \Cal S |a\cap
b|=|a\setminus b|=\kappa\}$ However,$\exists \kappa>\aleph_0$ $s(\kappa
)>\kappa ^+$ becomes a consid... | 1992-10-27 | 2008-02-03 | [
"math.LO"
] | Jind\v{r}ich Zapletal |
math/9210203 | Reflection and Weakly Collectionwise Hausdorff Spaces | We show that square(theta) implies that there is a first countable
<theta-collectionwise Hausdorff space that is not weakly theta-collectionwise
Hausdorff. We also show that in the model obtained by Levy collapsing a weakly
compact (supercompact) cardinal to omega_2, first countable
aleph_1-collectionwise Hausdorff spa... | 1992-10-21 | 2008-02-03 | [
"math.LO"
] | Tim LaBerge and Avner Landver |
math/9210202 | The Complexity of the Core Model | We use the Sigma^1_3 absoluteness theorem to show that the complexity of the
statement "(omega,E)$ is isomorphic to an initial segment of the core model" is
Pi^1_4, and that the complexity of the statement "(omega,E)$ is isomorphic to a
member of the core model" is Delta^1_5. | 1992-10-07 | 2016-09-06 | [
"math.LO"
] | William J. Mitchell |
math/9209209 | Some Natural Internal Forcing Schemata Extending ZFC | We give arguments for and prove the consistency of some internal forcing
axioms. | 1992-09-25 | 2009-09-25 | [
"math.LO"
] | Garvin Melles (Hebrew University) |
math/9209210 | $^*$Forcing | Let $M$ be a transitive model of $ZFC$ and let ${\bf B}$ be a $M$-complete
Boolean algebra in $M.$ (In general a proper class.) We define a generalized
notion of forcing with such Boolean algebras, $^*$forcing. (A $^*$ forcing
extension of $M$ is a transitive set of the form $M[{\bf G}]$ where ${\bf G}$
is an $M$-compl... | 1992-09-25 | 2016-09-06 | [
"math.LO"
] | Garvin Melles (Hebrew University) |
math/9209208 | Meager-nowhere dense games (III): Remainder strategies | Player ONE chooses a meager set and player TWO, a nowhere dense set per
inning. They play $\omega$ many innings. ONE's consecutive choices must form a
(weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense
sets covers the union of the chosen meager sets. A strategy for TWO which
depends on know... | 1992-09-25 | 2009-09-25 | [
"math.LO"
] | Marion Scheepers |
math/9209207 | Finite Combinations of Baire Numbers | Let $\kappa$ be a regular cardinal. Consider the Baire numbers of the spaces
$(2^{\theta})_\kappa$ (functions from $\theta$ to 2 and the less than $\kappa$
topology) for various $\theta \geq \kappa$. Let l be the number of such
different Baire numbers. Models of set theory with l=1 or l=2 are known and it
is also known... | 1992-09-16 | 2008-02-03 | [
"math.LO"
] | Avner Landver |
math/9209218 | Pointwise compact and stable sets of measurable functions | In a series of papers, M.Talagrand, the second author and others investigated
at length the properties and structure of pointwise compact sets of measurable
functions. A number of problems, interesting in themselves and important for
the theory of Pettis integration, were solved subject to various special
axioms. It wa... | 1992-09-15 | 2016-09-06 | [
"math.LO",
"math.FA"
] | David H. Fremlin, Saharon Shelah |
math/9209205 | Perfect sets of random reals | We discuss the relationship between perfect sets of random reals, dominating
reals, and the product of two copies of the random algebra B. Recall that B is
the algebra of Borel sets of 2^omega modulo the null sets. Also given two
models M subseteq N of ZFC, we say that g in omega^omega cap N is a dominating
real over M... | 1992-09-15 | 2008-02-03 | [
"math.LO"
] | J\"org Brendle and Haim Judah |
math/9209206 | Amoeba-absoluteness and projective measurability | We study the relationship between Amoeba forcing (the partial order which
generically adds a measure one set of random reals) and projective
measurability. Given a universe V of set theory and a forcing notion P in V we
say that V is Sigma^1_n - P - absolute iff for every Sigma^1_n-sentence phi
with parameters in V we ... | 1992-09-15 | 2009-09-25 | [
"math.LO"
] | J\"org Brendle |
math/9209204 | $\mu$-complete Souslin trees on $\mu^+$ | We prove that $\mu=\mu^{<\mu}$, $2^\mu=\mu^+$ and ``there is a non reflecting
stationary subset of $\mu^+$ composed of ordinals of cofinality $<\mu$'' imply
that there is a $\mu$-complete Souslin tree on $\mu^+$. | 1992-09-10 | 2008-02-03 | [
"math.LO"
] | Menachem Kojman |
math/9209203 | Cardinal Characteristics and the Product of Countably Many Infinite
Cyclic Groups | Let P be the direct product of countably many copies of the additive group Z
of integers. We study, from a set-theoretic point of view, those subgroups of P
for which all homomorphisms to Z annihilate all but finitely many of the
standard unit vectors. Specifically, we relate the smallest possible size of
such a subgro... | 1992-09-08 | 2009-09-25 | [
"math.LO"
] | Andreas Blass |
math/9209202 | Finite left-distributive algebras and embedding algebras\endtitle | We consider algebras with one binary operation $\cdot$ and one generator
({\it monogenic}) and satisfying the left distributive law $a\cdot (b\cdot
c)=(a\cdot b)\cdot (a\cdot c)$. One can define a sequence of finite
left-distributive algebras $A_n$, and then take a limit to get an infinite
monogenic left-distributive a... | 1992-09-08 | 2021-02-09 | [
"math.LO"
] | Randall Dougherty and Thomas Jech |
math/9209201 | Non-existence of Universal Orders in Many Cardinals | Our theme is that not every interesting question in set theory is independent
of $ZFC$. We give an example of a first order theory $T$ with countable $D(T)$
which cannot have a universal model at $\aleph_1$ without CH; we prove in $ZFC$
a covering theorem from the hypothesis of the existence of a universal model
for so... | 1992-09-03 | 2009-09-25 | [
"math.LO"
] | Menachem Kojman and Saharon Shelah |
math/9207205 | Remark on the Failure of Martin's Axiom | Let m be the least cardinal k such that MA(k) fails. The only known model for
"m is singular" was constructed by Kunen. In Kunen's model cof(m)=omega_1. It
is unknown whether "omega_1 < cof(m) < m" is consistent. The purpose of this
paper is to present a proof of Kunen's result and to identify the difficulties
of gener... | 1992-07-31 | 2008-02-03 | [
"math.LO"
] | Avner Landver |
math/9207204 | Donder's Version of Revised Countable Support | Shelah introduced the revised countable support (RCS) iteration to iterate
semiproperness. This was an endpoint in the search for an iteration of a weak
condition, still implying that aleph1 is preserved.
Dieter Donder found a better manageable approach to this iteration, which is
presented here. | 1992-07-30 | 2009-09-25 | [
"math.LO"
] | Ulrich Fuchs |
math/9207203 | Covering games and the Banach-Mazur game: k-tactics | Given a free ideal J of subsets of a set X, we consider games where player
ONE plays an increasing sequence of elements of the sigma completion of J, and
TWO tries to cover the union of this sequence by playing one set at a time from
J. We describe various conditions under which player TWO has has a winning
strategy th... | 1992-07-25 | 2009-09-25 | [
"math.LO"
] | Tomek Bartoszynski, Winfried Just and Marion Scheepers |
math/9205208 | Many simple cardinal invariants | For g < f in omega^omega we define c(f,g) be the least number of uniform
trees with g-splitting needed to cover a uniform tree with f-splitting. We show
that we can simultaneously force aleph_1 many different values for different
functions (f,g). In the language of Blass: There may be aleph_1 many distinct
uniform Pi^0... | 1992-05-15 | 2016-09-06 | [
"math.LO"
] | Martin Goldstern, Saharon Shelah |
math/9205202 | Critical points in an algebra of elementary embeddings | Given two elementary embeddings from the collection of sets of rank less than
$\lambda$ to itself, one can combine them to obtain another such embedding in
two ways: by composition, and by applying one to (initial segments of) the
other. Hence, a single such nontrivial embedding $j$ generates an algebra of
embeddings v... | 1992-05-07 | 2021-02-09 | [
"math.LO"
] | Randall Dougherty |
math/9205201 | The Cardinality of the second uniform indiscernible | When the second uniform indiscernible is $\aleph_{2}$, the Martin-Solovay
tree only constructs countably many reals; this resolves a number of open
questions in descriptive set theory. | 1992-05-01 | 2008-02-03 | [
"math.LO"
] | Greg Hjorth |
math/9204210 | Reaping Numbers of Boolean Algebras | A subset $A$ of a Boolean algebra $B$ is said to be $(n,m)$-reaped if there
is a partition of unity $P \subset B$ of size $n$ such that the cardinality of
$\{b \in P: b \wedge a \neq \emptyset\}$ is greater than or equal to $m$ for
all $a\in A$. The reaping number $r_{n,m}(B)$ of a Boolean algebra $B$ is the
minimum ca... | 1992-04-23 | 2008-02-03 | [
"math.LO"
] | A. Dow, J Stepr\=ans and W. S. Watson |
math/9204209 | Embeddings of Iteration Trees | This paper, dating from May 1991, contains preliminary (and unpublishable)
notes on investigations about iteration trees. They will be of interest only to
the specialist.
In the first two sections I define notions of support and embeddings for tree
iterations, proving for example that every tree iteration is a direct... | 1992-04-17 | 2016-09-06 | [
"math.LO"
] | William Mitchell |
math/9204208 | On Braid Words and Irreflexivity | The purpose of this note is to prove irreflexivity, and hence the linear
ordering, in ZFC, without some of the machinery used by Dehornoy. | 1992-04-16 | 2008-02-03 | [
"math.LO"
] | David M. Larue |
math/9204207 | On G\"odel's second incompleteness theorem | A very short proof of G\"odel's second incompleteness theorem (for set
theory, second order arithmetic etc.) | 1992-04-15 | 2009-09-25 | [
"math.LO"
] | Thomas Jech |
math/9204219 | Uniformization and the diversity of Whitehead groups | The connections between Whitehead groups and uniformization properties were
investigated by the third author in [Sh:98]. In particular it was essentially
shown there that there is a non-free Whitehead (respectively,
aleph_1-coseparable) group of cardinality aleph_1 if and only if there is a
ladder system on a stationar... | 1992-04-15 | 2016-09-06 | [
"math.LO",
"math.RA"
] | Paul C. Eklof, Alan H. Mekler, Saharon Shelah |
math/9204218 | Full reflection of stationary sets at regular cardinals | A stationary subset S of a regular uncountable cardinal kappa reflects fully
at regular cardinals if for every stationary set T subseteq kappa of higher
order consisting of regular cardinals there exists an alpha in T such that S
cap alpha is a stationary subset of alpha. We prove that the Axiom of Full
Reflection whic... | 1992-04-15 | 2008-02-03 | [
"math.LO"
] | Thomas Jech, Saharon Shelah |
math/9204206 | A short proof of the irreflexivity conjecture | Gives a short proof of Dehornoy's latest result. The same simple argument
(and more) was discovered by Laver's student Larue. | 1992-04-15 | 2008-02-03 | [
"math.LO"
] | Thomas Jech |
math/9204203 | A division Algorithm for the Free Left Distributive Algebra | The normal form theorem, proved in R. Laver, On the left distributive law and
the freeness of an algebra of elementary embeddings, Advances in Mathematics 91
(1992), 209-231, for the free algebra $\Cal A$ on one generator $x$ satisfying
the left distributive law $a(bc) = (ab)(ac)$ is extended by showing that
members of... | 1992-04-13 | 2016-09-06 | [
"math.LO"
] | Richard Laver |
math/9204205 | Maximal Chains in {}^\omega\omega and Ultrapowers of the Integers | Various questions posed by P. Nyikos concerning ultrafilters on $\omega$ and
chains in the partial order $(\omega,<^*)$ are answered. The main tool is the
oracle chain condition and variations of it. | 1992-04-13 | 2016-09-06 | [
"math.LO"
] | Saharon Shelah and Juris Stepr\=ans |
math/9204204 | On the Algebra of Elementary Embeddings of a Rank into Inself | Let $j:V_\lambda---> V_\lambda$ be an elementary embedding, with critical
point $\kappa$, and let $f(n)$ be the number of critical points of embeddings
in the algebra generated by $j$ which lie between $j^n(\kappa)$ and
$j^{n+1}(\kappa)$. It is shown that $f(n)$ is finite for all $n$. | 1992-04-13 | 2008-02-03 | [
"math.LO"
] | Richard Laver |
math/9204202 | On the Singular Cardinal Hypothesis | We use the core model for sequences of measures to prove a new lower bound
for the consistency strength of the failure of the SCH:
THEOREM
(i) If there is a singular strong limit cardinal $\kappa$ such that $2^\kappa
> kappa^+$ then there is an inner model with a cardinal $\kappa$ such that for
all ordinals $\alpha... | 1992-04-06 | 2016-09-06 | [
"math.LO"
] | William J. Mitchell |
math/9202205 | Constructing strongly equivalent nonisomorphic models for unsuperstable
theories. Part B | We study how equivalent nonisomorphic models of unsuperstable theories can
be. We measure the equivalence by Ehrenfeucht-Fraisse games. This paper
continues [HySh:474]. | 1992-02-15 | 2009-09-25 | [
"math.LO"
] | Tapani Hyttinen, Saharon Shelah |
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