Geometry Of Banach Spaces And Related Fields

Author : Gilles Godefroy,Mohammad Sal Moslehian,Juan Benigno Seoane-Sepúlveda
Publisher : American Mathematical Society
Page : 358 pages
File Size : 41,5 Mb
Release : 2024-03-27
Category : Mathematics
ISBN : 9781470475703

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Geometry of Banach Spaces and Related Fields by Gilles Godefroy,Mohammad Sal Moslehian,Juan Benigno Seoane-Sepúlveda Pdf

This book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography. This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.

Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 55,8 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 : J. Diestel
Publisher : Springer
Page : 298 pages
File Size : 52,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540379133

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

Author : Kazimierz Goebel,Stanislaw Prus
Publisher : Oxford University Press
Page : 256 pages
File Size : 41,6 Mb
Release : 2018-09-06
Category : Mathematics
ISBN : 9780192562326

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Elements of Geometry of Balls in Banach Spaces by Kazimierz Goebel,Stanislaw Prus Pdf

One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects includes: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory and others. The book presents basic facts from this field.

Author : Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer
Page : 169 pages
File Size : 44,7 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 : Antonio José Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer Nature
Page : 621 pages
File Size : 45,9 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 : Pandelis Dodos
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 46,8 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 : Beata Randrianantoanina,Narcisse Randrianantoanina
Publisher : Walter de Gruyter
Page : 465 pages
File Size : 48,9 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110918298

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Banach Spaces and their Applications in Analysis by Beata Randrianantoanina,Narcisse Randrianantoanina Pdf

In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.

Author : Simeon Reich,David Shoiykhet
Publisher : Imperial College Press
Page : 372 pages
File Size : 49,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860947148

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Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces by Simeon Reich,David Shoiykhet Pdf

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces. Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments. Contents: Mappings in Metric and Normed Spaces; Differentiable and Holomorphic Mappings in Banach Spaces; Hyperbolic Metrics on Domains in Complex Banach Spaces; Some Fixed Point Principles; The DenjoyOCoWolff Fixed Point Theory; Generation Theory for One-Parameter Semigroups; Flow-Invariance Conditions; Stationary Points of Continuous Semigroups; Asymptotic Behavior of Continuous Flows; Geometry of Domains in Banach Spaces."

Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 50,9 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817645960

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History of Banach Spaces and Linear Operators by Albrecht Pietsch Pdf

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.

Author : I. Cioranescu
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400921214

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Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems by I. Cioranescu Pdf

One service mathematics has rendered the 'Et moi ... - si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Terry J. Morrison
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 45,6 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118031247

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Functional Analysis by Terry J. Morrison Pdf

A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.

Author : P. F. X. Müller,Walter Schachermayer
Publisher : Unknown
Page : 288 pages
File Size : 43,7 Mb
Release : 1991
Category : Banach spaces
ISBN : 110736664X

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Geometry of Banach Spaces by P. F. X. Müller,Walter Schachermayer Pdf

This volume reflects the progress made in many branches of recent research in Banach space theory and illustrates its interplay with other areas of analysis.

Author : Gilles Pisier
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 44,6 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821807101

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Factorization of Linear Operators and Geometry of Banach Spaces by Gilles Pisier Pdf

This book surveys the considerable progress made in Banach space theory as a result of Grothendieck's fundamental paper ""Resume De la Theorie Metrique des Produits Tensoriels Topologiques"". The author examines the central question of which Banach spaces $X$ and $Y$ have the property that every bounded operator from $X$ to $Y$ factors through a Hilbert space, in particular when the operators are defined on a Banach lattice, a $C^*$-algebra or the disc algebra and $H^\infty$. He reviews the six problems posed at the end of Grothendieck's paper, which have now all been solved (except perhaps the exact value of Grothendieck's constant), and includes the various results which led to their solution. The last chapter contains the author's construction of several Banach spaces such that the injective and projective tensor products coincide; this gives a negative solution to Grothendieck's sixth problem.Although the book is aimed at mathematicians working in functional analysis, harmonic analysis and operator algebras, its detailed and self-contained treatment makes the material accessible to nonspecialists with a grounding in basic functional analysis. In fact, the author is particularly concerned to develop very recent results in the geometry of Banach spaces in a form that emphasizes how they may be applied in other fields, such as harmonic analysis and $C^*$-algebras.

Author : Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 54,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475734805

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Functional Analysis and Infinite-Dimensional Geometry by Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler Pdf

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.