Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by N. L. Randrianarivony
by Dale Alspach 12 Nov '04

12 Nov '04

This is an announcement for the paper "Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space" by N. L. Randrianarivony. Abstract: A map f between two metric spaces (X,d_1) and (Y,d_2) is called a coarse embedding of X into Y if there exist two nondecreasing functions phi_1, phi_2:[0,\infty) --> [0,\infty) such that: phi_1(d_1(x,y)) \leq d_2(f(x),f(y)) \leq phi_2(d_1(x,y)) for all x, y in X, and phi_1(t) tends to \infty as t tends to \infty. We characterize those quasi-Banach spaces that have a coarse embedding into a Hilbert space. Archive classification: Functional Analysis; Metric Geometry Remarks: 3 pages The source file(s), LovaGenAMM.4.tex: 6257 bytes, is(are) stored in gzipped form as 0411269.gz with size 3kb. The corresponding postcript file has gzipped size 25kb. Submitted from: nirina(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0411269 or http://arXiv.org/abs/math.FA/0411269 or by email in unzipped form by transmitting an empty message with subject line uget 0411269 or in gzipped form by using subject line get 0411269 to: math(a)arXiv.org.

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Abstract of a paper by Guoliang Yu
by Dale Alspach 12 Nov '04

12 Nov '04

This is an announcement for the paper "Hyperbolic groups admit proper affine isometric actions on $l^p$-spaces" by Guoliang Yu. Abstract: In this paper, we show that hyperbolic groups admit proper affine isometric actions on $l^p$-spaces. Archive classification: Group Theory; Operator Algebras Remarks: 10 pages (to appear in GAFA) The source file(s), hyplp.tex: 17579 bytes, is(are) stored in gzipped form as 0411234.gz with size 6kb. The corresponding postcript file has gzipped size 37kb. Submitted from: gyu(a)math.vanderbilt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.GR/0411234 or http://arXiv.org/abs/math.GR/0411234 or by email in unzipped form by transmitting an empty message with subject line uget 0411234 or in gzipped form by using subject line get 0411234 to: math(a)arXiv.org.

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Abstract of a paper by Michael Megrelishvili
by Dale Alspach 08 Nov '04

08 Nov '04

This is an announcement for the paper "Fragmentability and representations of flows" by Michael Megrelishvili. Abstract: Our aim is to study weak star continuous representations of semigroup actions into the duals of ``good'' (e.g., reflexive and Asplund) Banach spaces. This approach leads to flow analogs of Eberlein and Radon-Nikodym compacta and a new class of functions (Asplund functions) which intimately is connected with Asplund representations and includes the class of weakly almost periodic functions. We show that a flow is weakly almost periodic iff it admits sufficiently many reflexive representations. One of the main technical tools in this paper is the concept of fragmentability (which actually comes from Namioka and Phelps) and widespreadly used in topological aspects of Banach space theory. We explore fragmentability as ``a generalized equicontinuity'' of flows. This unified approach allows us to obtain several dynamical applications. We generalize and strengthen some results of Akin-Auslander-Berg, Shtern, Veech-Troallic-Auslander and Hansel-Troallic. We establish that frequently, for linear G-actions, weak and strong topologies coincide on, not necessarily closed, G-minimal subsets. For instance such actions are ``orbitwise Kadec``. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: 54H15; 43A60 Citation: Topology Proceedings, 27:2, 2003, 497-544 Remarks: 30 pages The source file(s), RN.tex: 154972 bytes, diagrams.tex: 116119 bytes, is(are) stored in gzipped form as 0411112.tar.gz with size 82kb. The corresponding postcript file has gzipped size 129kb. Submitted from: megereli(a)math.biu.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0411112 or http://arXiv.org/abs/math.FA/0411112 or by email in unzipped form by transmitting an empty message with subject line uget 0411112 or in gzipped form by using subject line get 0411112 to: math(a)arXiv.org.

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Abstract of a paper by Ravi Montenegro
by Dale Alspach 05 Nov '04

05 Nov '04

This is an announcement for the paper "A sharp isoperimetric bound for convex bodies" by Ravi Montenegro. Abstract: We consider the problem of lower bounding a generalized Minkowski measure of subsets of a convex body with a log-concave probability measure, conditioned on the set size. A bound is given in terms of diameter and set size, which is sharp for all set sizes, dimensions, and norms. In the case of uniform density a stronger theorem is shown which is also sharp. Archive classification: Functional Analysis; Metric Geometry; Probability Mathematics Subject Classification: 52A40 The source file(s), iso.bbl: 1295 bytes, iso.tex: 41335 bytes, is(are) stored in gzipped form as 0411018.tar.gz with size 14kb. The corresponding postcript file has gzipped size 52kb. Submitted from: monteneg(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0411018 or http://arXiv.org/abs/math.FA/0411018 or by email in unzipped form by transmitting an empty message with subject line uget 0411018 or in gzipped form by using subject line get 0411018 to: math(a)arXiv.org.

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Abstract of a paper by S. A. Argyros, J. Lopez-Abad and S. Todorcevic
by Dale Alspach 05 Nov '04

05 Nov '04

This is an announcement for the paper "A class of Banach spaces with few non strictly singular operators" by S. A. Argyros, J. Lopez-Abad and S. Todorcevic. Abstract: We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$. Archive classification: Functional Analysis; Logic Mathematics Subject Classification: 46B20; 03E05 Remarks: 52 pages, 1 figure The source file(s), om1hi.tex: 254359 bytes, om1hi1.eps: 181035 bytes, is(are) stored in gzipped form as 0312522.tar.gz with size 117kb. The corresponding postcript file has gzipped size 333kb. Submitted from: jlopez(a)crm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0312522 or http://arXiv.org/abs/math.FA/0312522 or by email in unzipped form by transmitting an empty message with subject line uget 0312522 or in gzipped form by using subject line get 0312522 to: math(a)arXiv.org.

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Chair in Mathematics (Analysis)
by Dale Alspach 03 Nov '04

03 Nov '04

CHAIR IN PURE MATHEMATICS AT LANCASTER UNIVERSITY Broad field: Pure Mathematics Duration: Indefinite Position: Professor Institution: Department of Mathematics and Statistics, Lancaster University Starting date: 1.4.05 (or preferably before 1.9.05) Area(s) preferred: Analysis Contact person(s): Professor S.C. Power, s.power(a)lancaster.ac.uk Application deadline: 7.1.05 Other comments: Job reference number A374 Full details: Personnel Services, Lancaster University Telephone: (01524) 846549 WWW: http://www.personnel.lancs.ac.uk/vacancydets.aspx?jobid=A374

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Abstract of a paper by V.Yaskin
by Dale Alspach 27 Oct '04

27 Oct '04

This is an announcement for the paper "The Busemann-Petty problem in hyperbolic and spherical spaces" by V.Yaskin. Abstract: The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer to this problem is affirmative if $n\le 4$ and negative if $n\ge 5$. We study this problem in hyperbolic and spherical spaces. Archive classification: Functional Analysis Mathematics Subject Classification: 52Axx Remarks: 16 pages, 2 figures The source file(s), HyperbolicBP.tex: 38485 bytes, pic02.eps: 9386 bytes, picForVlad2.eps: 3824 bytes, is(are) stored in gzipped form as 0410501.tar.gz with size 15kb. The corresponding postcript file has gzipped size 68kb. Submitted from: yaskinv(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0410501 or http://arXiv.org/abs/math.FA/0410501 or by email in unzipped form by transmitting an empty message with subject line uget 0410501 or in gzipped form by using subject line get 0410501 to: math(a)arXiv.org.

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Abstract of a paper by A.Koldobsky, V.Yaskin and M.Yaskina
by Dale Alspach 27 Oct '04

27 Oct '04

This is an announcement for the paper "Modified Busemann-Petty problem on sections of convex bodies" by A.Koldobsky, V.Yaskin and M.Yaskina. Abstract: The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer is affirmative if $n\le 4$ and negative if $n\ge 5$. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions. Archive classification: Functional Analysis Mathematics Subject Classification: 52Axx Remarks: 17 pages The source file(s), modBP.tex: 33931 bytes, is(are) stored in gzipped form as 0410496.gz with size 10kb. The corresponding postcript file has gzipped size 64kb. Submitted from: yaskinv(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0410496 or http://arXiv.org/abs/math.FA/0410496 or by email in unzipped form by transmitting an empty message with subject line uget 0410496 or in gzipped form by using subject line get 0410496 to: math(a)arXiv.org.

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Abstract of a paper by W. B. Johnson and N. L. Randrianarivony
by Dale Alspach 20 Oct '04

20 Oct '04

This is an announcement for the paper "$\ell_p$ (p>2) does not coarsely embed into a Hilbert space" by W. B. Johnson and N. L. Randrianarivony. Abstract: A coarse embedding of a metric space X into a metric space Y is a map f: X-->Y satisfying for every x, y in X: \phi_1(d(x,y)) \leq d(f(x),f(y)) \leq \phi_2(d(x,y)) where \phi_1 and \phi_2 are nondecreasing functions on [0,\infty) with values in [0,\infty), with the condition that \phi_1(t) tends to \infty as t tends to \infty. We show that \ell_p does not coarsely embed in a Hilbert space for 2<p<\infty. Archive classification: Functional Analysis Remarks: 10 pages The source file(s), coarselpl2.9.tex: 14916 bytes, is(are) stored in gzipped form as 0410427.gz with size 5kb. The corresponding postcript file has gzipped size 36kb. Submitted from: nirina(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0410427 or http://arXiv.org/abs/math.FA/0410427 or by email in unzipped form by transmitting an empty message with subject line uget 0410427 or in gzipped form by using subject line get 0410427 to: math(a)arXiv.org.

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Abstract of a paper by Assaf Naor, Yuval Peres, Oded Schramm and Scott Sheffield
by Dale Alspach 20 Oct '04

20 Oct '04

This is an announcement for the paper "Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces" by Assaf Naor, Yuval Peres, Oded Schramm and Scott Sheffield. Abstract: A metric space $X$ has {\em Markov type\/} $2$, if for any reversible finite-state Markov chain $\{Z_t\}$ (with $Z_0$ chosen according to the stationary distribution) and any map $f$ from the state space to $X$, the distance $D_t$ from $f(Z_0)$ to $f(Z_t)$ satisfies $\E(D_t^2) \le K^2\, t\, \E(D_1^2)$ for some $K=K(X)<\infty$. This notion is due to K.\,Ball (1992), who showed its importance for the Lipschitz extension problem. However until now, only Hilbert space (and its bi-Lipschitz equivalents) were known to have Markov type 2. We show that every Banach space with modulus of smoothness of power type $2$ (in particular, $L_p$ for $p>2$) has Markov type $2$; this proves a conjecture of Ball. We also show that trees, hyperbolic groups and simply connected Riemannian manifolds of pinched negative curvature have Markov type $2$. Our results are applied to settle several conjectures on Lipschitz extensions and embeddings. In particular, we answer a question posed by Johnson and Lindenstrauss in 1982, by showing that for $1<q<2<p<\infty$, any Lipschitz mapping from a subset of $L_p$ to $L_q$ has a Lipschitz extension defined on all of $L_p$. Archive classification: Functional Analysis; Probability Mathematics Subject Classification: 46B99 (primary), 60B99 (secondary) Remarks: 27 pages The source file(s), Mtype.tex: 95789 bytes, lang.fig: 18215 bytes, lang.pstex: 17247 bytes, lang.pstex_t: 859 bytes, is(are) stored in gzipped form as 0410422.tar.gz with size 38kb. The corresponding postcript file has gzipped size 129kb. Submitted from: anaor(a)microsoft.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0410422 or http://arXiv.org/abs/math.FA/0410422 or by email in unzipped form by transmitting an empty message with subject line uget 0410422 or in gzipped form by using subject line get 0410422 to: math(a)arXiv.org.

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