Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Guo TieXin and Zeng XiaoLin
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "An $L^{0}({\cal F},R)-$valued function's intermediate value theorem and its applications to random uniform convexity" by Guo TieXin and Zeng XiaoLin. Abstract: Let $(\Omega,{\cal F},P)$ be a probability space and $L^{0}({\cal F},R)$ the algebra of equivalence classes of real-valued random variables on $(\Omega,{\cal F},P)$. When $L^{0}({\cal F},R)$ is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from $L^{0}({\cal F},R)$ to $L^{0}({\cal F},R)$. As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module $(S,\|\cdot\|)$ is random uniformly convex iff $L^{p}(S)$ is uniformly convex for each fixed positive number $p$ such that $1<p<+\infty$. Archive classification: math.FA Mathematics Subject Classification: 46A22, 46B20, 46E30 Remarks: 14pages Submitted from: xlinzeng(a)ss.buaa.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.3775 or http://arXiv.org/abs/1103.3775

1 0

Abstract of a paper by Luong Dang Ky
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "New Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators" by Luong Dang Ky. Abstract: We introduce a new class of Hardy spaces $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\'ia-Cuerva, Str\"omberg, and Torchinsky. Here, $\varphi: \mathbb R^n\times [0,\infty)\to [0,\infty)$ is a function such that $\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty$ weight. A function $f$ belongs to $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$ if and only if its maximal function $f^*$ is so that $x\mapsto \varphi(x,|f^*(x)|)$ is integrable. Such a space arises naturally for instance in the description of the product of functions in $H^1(\mathbb R^n)$ and $BMO(\mathbb R^n)$ respectively (see \cite{BGK}). We characterize these spaces via the grand maximal function and establish their atomic decomposition. We characterize also their dual spaces. The class of pointwise multipliers for $BMO(\mathbb R^n)$ characterized by Nakai and Yabuta can be seen as the dual of $L^1(\mathbb R^n)+ H^{\rm log}(\mathbb R^n)$ where $ H^{\rm log}(\mathbb R^n)$ is the Hardy space of Musielak-Orlicz type related to the Musielak-Orlicz function $\theta(x,t)=\displaystyle\frac{t}{\log(e+|x|)+ \log(e+t)}$. Furthermore, under additional assumption on $\varphi(\cdot,\cdot)$ we prove that if $T$ is a sublinear operator and maps all atoms into uniformly bounded elements of a quasi-Banach space $\mathcal B$, then $T$ uniquely extends to a bounded sublinear operator from $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$ to $\mathcal B$. These results are new even for the classical Hardy-Orlicz spaces on $\mathbb R^n$. Archive classification: math.CA math.FA Submitted from: dangky(a)math.cnrs.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.3757 or http://arXiv.org/abs/1103.3757

1 0

Informal analysis seminar at Kent State (resend)
by Dale Alspach 07 Apr '11

07 Apr '11

Some information was omitted from the previous post. This is an announcement of a two-day long informal analysis seminar at Kent State which will be held next Thursday and Friday, April 14 and 15. More information about the schedule of talks is available at http://www.kent.edu/math/upload/informal-analysis-sem-announcement.pdf Richard M. Aron aron(a)math.kent.edu

1 0

Informal analysis seminar at Kent State
by Dale Alspach 07 Apr '11

07 Apr '11

This is an announcement of an two-day long informal analysis seminar at Kent State which will be held next Thursday and Friday, April 14 and 15. Richard M. Aron aron(a)math.kent.edu

1 0

Submission
by Rich, Meredith, Springer US 07 Apr '11

07 Apr '11

The following book is published: Banach Space Theory: The Basis for Linear and Nonlinear Analysis by Marián Fabian, Petr Habala, Petr Hájek, Vincente Montesinos, Václav Zizler, 1st Edition, 2011. [XIV, 822 p. 40 illus. Hardcover, ISBN 978-1-4419-7514-0] More information: http://www.springer.com/mathematics/analysis/book/978-1-4419-7514-0 Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book. --------- Meredith Rich Springer Science+Business Media Mathematics Series Coordinator for Springer Proceedings in Mathematics Editorial Assistant to Vaishali Damle ---------- 233 Spring Street | New York NY 10013 (tel) 1-212-620-8451 (fax) 1-212-460-1565 Meredith.Rich(a)Springer.com --------- http://www.springer.com

1 0

Abstract of a paper by Nazim I. Mahmudov
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

This is an announcement for the paper "Korovkin type theorem for iterates of certain positive linear operators" by Nazim I. Mahmudov. Abstract: In this paper we prove that if T:C[0,1]→C[0,1] is a positive linear operator with T(e₀)=1 and T(e₁)-e₁ does not change the sign, then the iterates T^{m} converges to some positive linear operator T^{∞} :C[0,1]→C[0,1] and we derive quantitative estimates in terms of modulii of smoothness. This result enlarges the class of operators for which the limit of the iterates can be computed and the quantitative estimates of iterates can be given. Archive classification: math.FA Submitted from: mahmudov2009(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.2918 or http://arXiv.org/abs/1103.2918

1 0

Abstract of a paper by Dirk Werner
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

This is an announcement for the paper "Nigel Kalton's work in isometrical Banach space theory" by Dirk Werner. Abstract: This paper surveys some of the late Nigel Kalton's contributions to Banach space theory. The paper is written for the Nigel Kalton Memorial Website http://mathematics.missouri.edu/kalton/, which is scheduled to go online in summer 2011. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B03, 46B28 Submitted from: werner(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.3153 or http://arXiv.org/abs/1103.3153

1 0

Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

This is an announcement for the paper "On a difference between quantitative weak sequential completeness and the quantitative Schur property" by Ondrej F.K. Kalenda and Jiri Spurny. Abstract: We study quantitative versions of the Schur property and weak sequential completeness, proceeding thus with investigations started by G. Godefroy, N. Kalton and D. Li and continued by H. Pfitzner and the authors. We show that the Schur property of $\ell_1$ holds quantitatively in the strongest possible way and construct an example of a Banach space which is quantitatively weakly sequentially complete, has the Schur property but fails the quantitative form of the Schur property. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B25 Remarks: 7 pages Submitted from: kalenda(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.2975 or http://arXiv.org/abs/1103.2975

1 0

Abstract of a paper by Boaz Klartag and Emanuel Milman
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

This is an announcement for the paper "Centroid bodies and the logarithmic Laplace transform - A unified approach" by Boaz Klartag and Emanuel Milman. Abstract: We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's psi-2 constant is obtained. Along the way, we present some new bounds on the volume of L_p-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the L_p-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author. Archive classification: math.FA Submitted from: klartagb(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.2985 or http://arXiv.org/abs/1103.2985

1 0

Abstract of a paper by Gilles Pisier
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

This is an announcement for the paper "Completely co-bounded Schur multipliers" by Gilles Pisier. Abstract: A linear map $u\colon \ E\to F$ between operator spaces is called completely co-bounded if it is completely bounded as a map from $E$ to the opposite of $F$. We give several simple results about completely co-bounded Schur multipliers on $B(\ell_2)$ and the Schatten class $S_p$. We also consider Herz-Schur multipliers on groups. Archive classification: math.FA math.OA 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/1103.2108 or http://arXiv.org/abs/1103.2108

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