Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Mikael de la Salle
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Towards Banach space strong property (T) for SL(3,R)" by Mikael de la Salle. Abstract: We prove that SL(3,R) has strong property (T) in Lafforgue's sense with respect to the Banach spaces that are \theta>0 interpolation spaces (for the Lions-Calder\'on complex interpolation method) between an arbitrary Banach space and a Banach space with sufficiently good type and cotype. As a consequence, for such a Banach space X, SL(3,R) and its lattices have the fixed point property (F_X) of Bader--Furman--Gelander--Monod, and the expanders contructed from SL(3,Z) do not admit a coarse embedding into X. We also prove a quantitative decay of matrix coefficients (Howe-Moore property) for representations with small exponential growth of SL(3,R) on X. This class of Banach spaces contains the classical superreflexive spaces and some nonreflexive spaces as well. We see no obstruction for this class to be equal to all spaces with nontrivial type. Archive classification: math.GR math.FA math.MG Remarks: 31 pages, 3 figures. Comments welcome! Submitted from: delasall(a)phare.normalesup.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.2475 or http://arXiv.org/abs/1307.2475

1 0

Abstract of a paper by Daniel Cariello and Juan B. Seoane-Sepulveda
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Basic sequences and spaceability in $\ell_p$ spaces" by Daniel Cariello and Juan B. Seoane-Sepulveda. Abstract: Let $X$ be a sequence space and denote by $Z(X)$ the subset of $X$ formed by sequences having only a finite number of zero coordinates. We study algebraic properties of $Z(X)$ and show (among other results) that (for $p \in [1,\infty]$) $Z(\ell_p)$ does not contain infinite dimensional closed subspaces. This solves an open question originally posed by R. M. Aron and V. I. Gurariy in 2003 on the linear structure of $Z(\ell_\infty)$. In addition to this, we also give a thorough analysis of the existing algebraic structures within the set $X \setminus Z(X)$ and its algebraic genericity. Archive classification: math.FA Remarks: 17 pages Submitted from: jseoane(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.2508 or http://arXiv.org/abs/1307.2508

1 0

Abstract of a paper by Aude Dalet
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Free spaces over countable compact metric spaces" by Aude Dalet. Abstract: We prove that the Lipschitz-free space over a countable compact metric space is isometric to a dual space and has the metric approximation property. Archive classification: math.FA Submitted from: aude.dalet(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.0735 or http://arXiv.org/abs/1307.0735

1 0

Abstract of a paper by Maria Acosta, Julio Becerra, Yun Sung Choi, Maciej Ciesielski, Sun Kwang Kim, Han Ju Lee, and Miguel Martin
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "The Bishop-Phelps-Bollob\'as property for operators between spaces of continuous functions" by Maria Acosta, Julio Becerra, Yun Sung Choi, Maciej Ciesielski, Sun Kwang Kim, Han Ju Lee, and Miguel Martin. Abstract: We show that the space of bounded and linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollob\'as property. A similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and Hausdorff topological space into a uniformly convex space, and for the class of compact operators from a Banach space into a predual of an $L_1$-space. Archive classification: math.FA Mathematics Subject Classification: 46B04 Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.6740 or http://arXiv.org/abs/1306.6740

1 0

SUMIRFAS Schedule
by Bill Johnson 20 Jul '13

20 Jul '13

Please see the attached schedule for SUMIRFAS, August 2-4, 2013, at Texas A&M University. Bill Johnson

1 0

SUMIRFAS
by Bill Johnson 01 Jul '13

01 Jul '13

1st ANNOUNCEMENT OF SUMIRFAS 2013 The Informal Regional Functional Analysis Seminar August 2-4 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, whose URL is http://www.math.tamu.edu/~kerr/workshop/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 169. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html. Coffee and refreshments will be available in Blocker 148. SUMIRFAS 2013 is dedicated to the memory of Ted Odell, who was one of the organizers of the UTAMIRFAS, the predecessor of SUMIRFAS. Ted served with distinction on the advisory board of the Workshop from its beginning until his untimely passing in January. The Plenary speakers at SUMIRFAS 2013 are Stephen Dilworth, Steve Jackson, Masoud Khalkhali, Thomas Schlumprecht, Nicole Tomczak-Jaegermann, and Wilhelm Winter. Other speakers include Tim Rainone, Paul Skoufranis, and John Williams. August 5-9 there will be a Concentration Week on "Dynamics, Geometry, and Operator Algebras", organized by David Kerr and Guoliang Yu. This Concentration Week aims to promote connections between nuclearity, nuclear dimension, group C*-algebras and crossed products, topological and measurable dynamics, algebraic dynamics, entropy, dimensional ideas from coarse geometry, and K-theory with applications to topology. The program will feature lecture series by David Kerr, Stuart White, and Rufus Willett. The URL for this Concentration Week is http://www.math.tamu.edu/~kerr/concweek13/ Immediately preceding SUMIRFAS, on August 1, there will be a celebration of "The Mathematical Legacy of Ted Odell", organized by Thomas Schlumprecht. The URL for this activity is http://math.slu.edu/~freeman/LegacyConference/ The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Kerr <kerr(a)math.tamu.edu>, or Gilles Pisier <pisier(a)math.tamu.edu>. For information about the Concentration Week on "Dynamics, Geometry, and Operator Algebras" contact David Kerr <kerr(a)math.tamu.edu>. For information about the day devoted to "The Mathematical Legacy of Ted Odell" contact Thomas Schlumprecht <schlump(a)math.tamu.edu>

1 0

Abstract of a paper by Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "Radon-Nikod\'ym property and thick families of geodesics" by Mikhail I. Ostrovskii. Abstract: Banach spaces without the Radon-Nikod\'ym property are characterized as spaces containing bilipschitz images of thick families of geodesics defined as follows. A family $T$ of geodesics joining points $u$ and $v$ in a metric space is called {\it thick} if there is $\alpha>0$ such that for every $g\in T$ and for any finite collection of points $r_1,\dots,r_n$ in the image of $g$, there is another $uv$-geodesic $\widetilde g\in T$ satisfying the conditions: $\widetilde g$ also passes through $r_1,\dots,r_n$, and, possibly, has some more common points with $g$. On the other hand, there is a finite collection of common points of $g$ and $\widetilde g$ which contains $r_1,\dots,r_n$ and is such that the sum of maximal deviations of the geodesics between these common points is at least $\alpha$. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B22, 46B85, 54E35 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.5807 or http://arXiv.org/abs/1306.5807

1 0

Abstract of a paper by Gilles Pisier
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "On the metric entropy of the Banach-Mazur compactum" by Gilles Pisier. Abstract: We study of the metric entropy of the metric space $\cl B_n$ of all $n$-dimensional Banach spaces (the so-called Banach-Mazur compactum) equipped with the Banach-Mazur (multiplicative) ``distance" $d$. We are interested either in estimates independent of the dimension or in asymptotic estimates when the dimension tends to $\infty$. For instance, we prove that, if $N({\cl B_n},d, 1+\vp)$ is the smallest number of ``balls" of ``radius" $1+\vp$ that cover $\cl B_n$, then for any $\vp>0$ we have $$0<\liminf_{n\to \infty} \log\log N(\cl B_n,d,1+\vp)\le \limsup_{n\to \infty} \log\log N(\cl B_n,d,1+\vp)<\infty.$$ We also prove similar results for the matricial operator space analogues. Archive classification: math.FA Submitted from: pisier(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.5325 or http://arXiv.org/abs/1306.5325

1 0

Abstract of a paper by Adam Marcus, Daniel A Spielman, and Nikhil Srivastava
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "Interlacing families II: Mixed characteristic polynomials and a question of Kadison and Singer" by Adam Marcus, Daniel A Spielman, and Nikhil Srivastava. Abstract: We use the method of interlacing families of polynomials to prove Weaver's conjecture KS_2, which is known to imply a positive answer to a famous question of Kadison and Singer via Anderson's Paving Conjecture. Our proof goes through an analysis of the largest roots of a family of polynomials that we call the "mixed characteristic polynomials" of a collection of matrices. Archive classification: math.CO math.FA math.OA Submitted from: spielman(a)cs.yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.3969 or http://arXiv.org/abs/1306.3969

1 0

Abstract of a paper by Niushan Gao and Foivos Xanthos
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "Unbounded order convergence and application to martingales without probability" by Niushan Gao and Foivos Xanthos. Abstract: A net $(x_\alpha)_{\alpha\in \Gamma}$ in a vector lattice $X$ is unbounded order convergent (uo-convergent) to $x$ if $|x_\alpha-x| \wedge y \xrightarrow{{o}} 0$ for each $y \in X_+$, and is unbounded order Cauchy (uo-Cauchy) if the net $(x_\alpha-x_{\alpha'})_{\Gamma\times \Gamma}$ is uo-convergent to $0$. In the first part of this article, we study uo-convergent and uo-Cauchy nets in Banach lattices and use them to characterize Banach lattices with the positive Schur property and KB-spaces. In the second part, we use the concept of uo-Cauchy sequences to extend Doob's submartingale convergence theorems to a measure-free setting. Our results imply, in particular, that every norm bounded submartingale in $L_1(\Omega;F)$ is almost surely uo-Cauchy in $F$, where $F$ is an order continuous Banach lattice with a weak unit. Archive classification: math.FA Submitted from: foivos(a)ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.2563 or http://arXiv.org/abs/1306.2563

1 0

Jump to page:

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach