Renormings In Banach Spaces

Author : Antonio José Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer Nature
Page : 621 pages
File Size : 48,9 Mb
Release : 2022-08-23
Category : Mathematics
ISBN : 9783031086557

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Renormings in Banach Spaces by Antonio José Guirao,Vicente Montesinos,Václav Zizler Pdf

This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.

Author : Robert Deville,Gilles Godefroy,Vaclav Zizler
Publisher : Chapman & Hall/CRC
Page : 398 pages
File Size : 45,7 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015029738054

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Smoothness and Renormings in Banach Spaces by Robert Deville,Gilles Godefroy,Vaclav Zizler Pdf

The purpose of this book is to provide the reader with a self-contained treatment of the basic techniques of construction of equivalent norms on Banach spaces which enjoy special properties of convexity and smoothness. We also show how the existence of such norms relates to the structure of the space, and provide applications in various directions.

Author : Aníbal Moltó
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 54,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9783540850304

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A Nonlinear Transfer Technique for Renorming by Aníbal Moltó Pdf

Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis.

Author : J. Diestel
Publisher : Springer
Page : 298 pages
File Size : 53,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540379133

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Geometry of Banach Spaces - Selected Topics by J. Diestel Pdf

Author : Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 55,7 Mb
Release : 2007-10-04
Category : Mathematics
ISBN : 9780387689159

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Biorthogonal Systems in Banach Spaces by Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler Pdf

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

Author : Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer
Page : 169 pages
File Size : 45,5 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319335728

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Open Problems in the Geometry and Analysis of Banach Spaces by Antonio J. Guirao,Vicente Montesinos,Václav Zizler Pdf

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.

Author : Jesus M.F. Castillo,Manuel González
Publisher : Springer
Page : 280 pages
File Size : 46,9 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9783540695196

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Three-space Problems in Banach Space Theory by Jesus M.F. Castillo,Manuel González Pdf

This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.

Author : J. Lindenstrauss,L. Tzafriri
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 53,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662353479

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Classical Banach Spaces II by J. Lindenstrauss,L. Tzafriri Pdf

Author : Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
Publisher : Springer
Page : 614 pages
File Size : 41,9 Mb
Release : 2016-11-26
Category : Mathematics
ISBN : 9783319485201

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Analysis in Banach Spaces by Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis Pdf

The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.

Author : Pandelis Dodos
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 54,9 Mb
Release : 2010-05-10
Category : Mathematics
ISBN : 9783642121524

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Banach Spaces and Descriptive Set Theory: Selected Topics by Pandelis Dodos Pdf

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.

Author : Vladimir Kadets
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 53,8 Mb
Release : 1997-03-20
Category : Mathematics
ISBN : 3764354011

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Series in Banach Spaces by Vladimir Kadets Pdf

Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements.

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 54,6 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9781441975157

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Banach Space Theory by Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler Pdf

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.

Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 46,9 Mb
Release : 2001-08-15
Category : Mathematics
ISBN : 9780080532806

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Handbook of the Geometry of Banach Spaces by Anonim Pdf

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Author : Pilar Cembranos,Jose Mendoza
Publisher : Springer
Page : 124 pages
File Size : 53,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696391

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Banach Spaces of Vector-Valued Functions by Pilar Cembranos,Jose Mendoza Pdf

"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.

Author : Petr Hájek,Michal Johanis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 513 pages
File Size : 42,5 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110391992

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Smooth Analysis in Banach Spaces by Petr Hájek,Michal Johanis Pdf

This bookis aboutthe subject of higher smoothness in separable real Banach spaces.It brings together several angles of view on polynomials, both in finite and infinite setting.Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treatedherefor the first time in full detail, therefore this book may also serve as a reference book.