Banach Spaces

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Isometries On Banach Spaces

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Author : Richard J. Fleming
language : en
Publisher: CRC Press
Release Date : 2002-12-23

Isometries On Banach Spaces written by Richard J. Fleming and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-23 with Mathematics categories.

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric

Topics In Banach Space Theory

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Author : Fernando Albiac
language : en
Publisher: Taylor & Francis
Release Date : 2006-01-04

Topics In Banach Space Theory written by Fernando Albiac and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-04 with Mathematics categories.

This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems.

Sequences And Series In Banach Spaces

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Author : J. Diestel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Sequences And Series In Banach Spaces written by J. Diestel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.

An Introduction To Banach Space Theory

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Author : Robert E. Megginson
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-10-09

An Introduction To Banach Space Theory written by Robert E. Megginson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-09 with Mathematics categories.

This book is an introduction to the general theory of Banach spaces, designed to prepare the reader with a background in functional analysis that will enable him or her to tackle more advanced literature in the subject. The book is replete with examples, historical notes, and citations, as well as nearly 500 exercises.

History Of Banach Spaces And Linear Operators

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Author : Albrecht Pietsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31

History Of Banach Spaces And Linear Operators written by Albrecht Pietsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.

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.

Biorthogonal Systems In Banach Spaces

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Author : Petr Hajek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-04

Biorthogonal Systems In Banach Spaces written by Petr Hajek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-04 with Mathematics categories.

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.

Topics In Banach Space Theory

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Author : Fernando Albiac
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-28

Topics In Banach Space Theory written by Fernando Albiac and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-28 with Mathematics categories.

This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems.

Probability In Banach Spaces

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Author : Michel Ledoux
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Probability In Banach Spaces written by Michel Ledoux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

Introduction To Tensor Products Of Banach Spaces

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Author : Raymond A. Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-15

Introduction To Tensor Products Of Banach Spaces written by Raymond A. Ryan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-15 with Mathematics categories.

This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.

Introduction To Banach Spaces And Algebras

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Author : Graham Allan
language : en
Publisher: Oxford University Press
Release Date : 2010-11-04

Introduction To Banach Spaces And Algebras written by Graham Allan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-04 with Mathematics categories.

Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources. The book was edited for publication by Professor H. G. Dales of Leeds University, following the death of the author in August, 2007.