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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