Banach November 2010

banach@mathdept.okstate.edu

2 participants
16 discussions

Abstract of a paper by Christian Le Merdy and Quanhua Xu
by alspach＠math.okstate.edu 23 Nov '10

23 Nov '10

This is an announcement for the paper "Maximal theorems and square functions for analytic operators on Lp-spaces" by Christian Le Merdy and Quanhua Xu. Abstract: Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is positive (or contractively regular), we establish the boundedness of various Littlewood-Paley square functions associated with T. As a consequence we show maximal inequalities of the form $\norm{\sup_{n\geq 0}\, (n+1)^m\bigl\vert T^n(T-I)^m(x) \bigr\vert}_p\,\lesssim\, \norm{x}_p$, for any nonnegative integer m. We prove similar results in the context of noncommutative Lp-spaces. We also give analogs of these maximal inequalities for bounded analytic semigroups, as well as applications to R-boundedness properties. Archive classification: math.FA math.OA Mathematics Subject Classification: 47B38, 46L52, 46A60 Submitted from: clemerdy(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.1360 or http://arXiv.org/abs/1011.1360

1 0

Abstract of a paper by Olivier Guedon and Emanuel Milman
by alspach＠math.okstate.edu 23 Nov '10

23 Nov '10

This is an announcement for the paper "Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures" by Olivier Guedon and Emanuel Milman. Abstract: Given an isotropic random vector $X$ with log-concave density in Euclidean space $\Real^n$, we study the concentration properties of $|X|$. We show in particular that: \[ \P(|X| \geq (1+t) \sqrt{n}) \leq \exp(-c n^{\frac{1}{2}} \min(t^3,t)) \;\;\; \forall t > 0 ~, \] for some universal constant $c>0$. This improves the best known deviation results above the expectation on the thin-shell and mesoscopic scales due to Fleury and Klartag, respectively, and recovers the sharp large-deviation estimate of Paouris. Another new feature of our estimate is that it improves when $X$ is $\psi_\alpha$ ($\alpha \in (1,2]$), in precise agreement with the sharp Paouris estimates. The upper bound on the thin-shell width $\sqrt{\Var(|X|)}$ we obtain is of the order of $n^{1/3}$, and improves down to $n^{1/4}$ when $X$ is $\psi_2$. Our estimates thus continuously interpolate between a new best known thin-shell estimate and the sharp Paouris large-deviation one. Archive classification: math.FA Remarks: 23 pages Submitted from: emanuel.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.1360 or http://arXiv.org/abs/1011.1360

1 0

Abstract of a paper by Jan Vybiral
by alspach＠math.okstate.edu 23 Nov '10

23 Nov '10

This is an announcement for the paper "Average best $m$-term approximation" by Jan Vybiral. Abstract: We introduce the concept of average best $m$-term approximation widths with respect to a probability measure on the unit ball of $\ell_p^n$. We estimate these quantities for the embedding $id:\ell_p^n\to\ell_q^n$ with $0<p\le q\le \infty$ for the normalized cone and surface measure. Furthermore, we consider certain tensor product weights and show that a typical vector with respect to such a measure exhibits a strong compressible (i.e. nearly sparse) structure. Archive classification: math.FA math.NA math.ST stat.TH Mathematics Subject Classification: 41A46 (Primary) 46B20, 60B11 (Secondary) Remarks: 2 figures Submitted from: jan.vybiral(a)oeaw.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.0943 or http://arXiv.org/abs/1011.0943

1 0

Abstract of a paper by Jarno Talponen
by alspach＠math.okstate.edu 23 Nov '10

23 Nov '10

This is an announcement for the paper "Extracting long basic sequences from systems of dispersed vectors" by Jarno Talponen. Abstract: We study Banach spaces satisfying some geometric or structural properties involving tightness of transfinite sequences of nested linear subspaces. These properties are much weaker than WCG and closely related to Corson's property (C). Given a transfinite sequence of normalized vectors, which is dispersed or null in some sense, we extract a subsequence which is a biorthogonal sequence, or even a weakly null monotone basic sequence, depending on the setting. The Separable Complementation Property is established for spaces with an M-basis under rather weak geometric properties. We also consider an analogy of the Baire Category Theorem for the lattice of closed linear subspaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B26, 46Bxx, 46M40 Remarks: 17 pages Submitted from: talponen(a)cc.hut.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.0071 or http://arXiv.org/abs/1011.0071

1 0

Abstract of a paper by Nikolai Nikolski and Vasily Vasyunin
by alspach＠math.okstate.edu 23 Nov '10

23 Nov '10

This is an announcement for the paper "Invertibility threshold for $H^\infty$ trace algebras, and effective matrix inversions" by Nikolai Nikolski and Vasily Vasyunin. Abstract: For a given $\delta$, $0<\delta<1$, a Blaschke sequence $\sigma=\{\lambda_j\}$ is constructed such that every function $f$, $f\in H^\infty$, having $\delta<\delta_f=\inf_{\lambda\in\sigma}|f(\lambda)|\le\|f\|_\infty\le1$ is invertible in the trace algebra $H^\infty|\sigma$ (with a norm estimate of the inverse depending on $\delta_f$ only), but there exists $f$ with $\delta=\delta_f\le\|f\|_\infty\le1$, which does not. As an application, a counterexample to a stronger form of the Bourgain--Tzafriri restricted invertibility conjecture for bounded operators is exhibited, where an ``orthogonal (or unconditional) basis'' is replaced by a ``summation block orthogonal basis''. Archive classification: math.FA Submitted from: vasyunin(a)pdmi.ras.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.6090 or http://arXiv.org/abs/1010.6090

1 0

N. Kalton
by Fritz Gesztesy 10 Nov '10

10 Nov '10

Dear Colleagues, In addition to my original message about the website in honor of Nigel Kalton, appended below, I'd like to ask all co-authors of Nigel to send me pdf files of ALL their joint papers with him. Please send only journal pdf's, not preprint versions. After obtaining permission from publishers (we already have permission from some publishers), we will post these pdf files on the Kalton website. Many thanks for your cooperation, Fritz Gesztesy > From: "Gesztesy, Friedrich" <gesztesyf(a)missouri.edu> > Date: October 17, 2010 3:46:23 PM CDT > To: "banach(a)cauchy.math.okstate.edu" <banach(a)cauchy.math.okstate.edu> > Cc: "alspach(a)math.okstate.edu" <alspach(a)math.okstate.edu>, "Gesztesy, Friedrich" <gesztesyf(a)missouri.edu> > Subject: N. Kalton > > Dear Colleagues, > > The Department of Mathematics of the University of Missouri, Columbia, MO, is in the process of establishing a website in honor of Nigel Kalton, who passed away recently. > > The website will consist of several parts. We hope to be able to post downloadable pdf files of his works, supply a list of his students and co-authors, indicate his editorial activity, establish a photo gallery, and comment on some of his other significant activities, such as playing chess. We also plan to have a section in which students, collaborators, and friends will be able to recall fond reminiscences and express their appreciation of Nigel. > > Apart from alerting you to this activity, the purpose of this message is to solicit contributions you may be able to make to this Kalton Memorial Website, such as, photos, stories, reminiscences, etc. > > Please send all material to > > Fritz Gesztesy > Department of Mathematics > University of Missouri > Columbia, MO 65211 > USA > > E-mail: gesztesyf(a)missouri.edu > > > Thanks, and best regards, > Fritz Gesztesy PLEASE NOTE THE CHANGE OF E-MAIL ADDRESS: gesztesyf(a)missouri.edu Department of Mathematics, University of Missouri, Columbia, MO 65211, USA Office: (573) 882 4386 FAX: (573) 882 1869 Department: (573) 882 6221 Home: (573) 443 8913 E-mail: gesztesyf(a)missouri.edu http://www.math.missouri.edu/personnel/faculty/gesztesyf.html

1 0

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach November 2010