Series In Banach Spaces
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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.
Series In Banach Spaces
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Author : Vladimir Kadets
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Series In Banach Spaces written by Vladimir Kadets and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Sequences And Series In Banach Spaces
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Author : Joseph Diestel
language : en
Publisher:
Release Date : 1984-01
Sequences And Series In Banach Spaces written by Joseph Diestel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01 with Banach spaces categories.
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.
Smooth Analysis In Banach Spaces
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Author : Petr Hájek
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-29
Smooth Analysis In Banach Spaces written by Petr Hájek and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-29 with Mathematics categories.
This book is about the 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 treated here for the first time in full detail, therefore this book may also serve as a reference book.
Rearrangements Of Series In Banach Spaces
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Author : Vladimir M. Kadet͡s
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Rearrangements Of Series In Banach Spaces written by Vladimir M. Kadet͡s and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
In a contemporary course in mathematical analysis, the concept of series arises as a natural generalization of the concept of a sum over finitely many elements, and the simplest properties of finite sums carry over to infinite series. Standing as an exception among these properties is the commutative law, for the sum of a series can change as a result of a rearrangement of its terms. This raises two central questions: for which series is the commutative law valid, and just how can a series change upon rearrangement of its terms? Both questions have been answered for all finite-dimensional spaces, but the study of rearrangements of a series in an infinite-dimensional space continues to this day.In recent years, a close connection has been discovered between the theory of series and the so-called finite properties of Banach spaces, making it possible to create a unified theory from the numerous separate results. This book is the first attempt at such a unified exposition. This book would be an ideal textbook for advanced courses, for it requires background only at the level of standard courses in mathematical analysis and linear algebra and some familiarity with elementary concepts and results in the theory of Banach spaces. The authors present the more advanced results with full proofs, and they have included a large number of exercises of varying difficulty. A separate section in the last chapter is devoted to a detailed survey of open questions. The book should prove useful and interesting both to beginning mathematicians and to specialists in functional analysis.
Functional Analysis
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Author : Terry J. Morrison
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
Functional Analysis written by Terry J. Morrison and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
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.
Bases In Banach Spaces
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Author : Ivan Singer
language : en
Publisher: Springer
Release Date : 1970
Bases In Banach Spaces written by Ivan Singer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Classical Banach Spaces
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Author : Joram Lindenstrauss
language : en
Publisher: Springer
Release Date : 2006-11-15
Classical Banach Spaces written by Joram Lindenstrauss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added. Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers.
Banach Spaces Of Vector Valued Functions
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Author : Pilar Cembranos
language : en
Publisher: Springer
Release Date : 2006-11-14
Banach Spaces Of Vector Valued Functions written by Pilar Cembranos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
"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.