Sequences and Series in Banach Spaces
Author: J. Diestel
Publisher:
Published: 1984-02-28
Total Pages: 276
ISBN-13: 9781461252016
DOWNLOAD EBOOK →Author: J. Diestel
Publisher:
Published: 1984-02-28
Total Pages: 276
ISBN-13: 9781461252016
DOWNLOAD EBOOK →Author: Joseph Diestel
Publisher:
Published: 1984
Total Pages: 261
ISBN-13: 9787506201223
DOWNLOAD EBOOK →Author: J. Diestel
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 273
ISBN-13: 1461252008
DOWNLOAD EBOOK →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.
Author: Joseph Diestel
Publisher:
Published: 1984-01
Total Pages: 261
ISBN-13: 9783540908593
DOWNLOAD EBOOK →Author: Vladimir Kadets
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 162
ISBN-13: 3034891962
DOWNLOAD EBOOK →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: Sylvia Guerre-Delabriere
Publisher: CRC Press
Published: 1992-07-21
Total Pages: 234
ISBN-13: 9780824787233
DOWNLOAD EBOOK →Author: Pawan K. Jain
Publisher: Alpha Science Int'l Ltd.
Published: 1999
Total Pages: 162
ISBN-13: 9788173192395
DOWNLOAD EBOOK →This volume contains referred articles covering areas in classical as well as modern sequence space theory. The major topics covered are: classical sequence spaces; duals and matrix transformation; structure and topology; and applications. The book should be useful to postgraduates and the researchers working or intending to work in the areas of classical and the modern sequence space theory.
Author: J. Lindenstrauss
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 202
ISBN-13: 3642665578
DOWNLOAD EBOOK →The appearance of Banach's book [8] in 1932 signified the beginning of a syste matic study of normed linear spaces, which have been the subject of continuous research ever since. In the sixties, and especially in the last decade, the research activity in this area grew considerably. As a result, Ban:ach space theory gained very much in depth as well as in scope: Most of its well known classical problems were solved, many interesting new directions were developed, and deep connections between Banach space theory and other areas of mathematics were established. The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces, with an emphasis on the study of the structure of the classical Banach spaces, that is C(K) and Lip.) and related spaces. We did not attempt to write a comprehensive survey of Banach space theory, or even only of the theory of classical Banach spaces, since the amount of interesting results on the subject makes such a survey practically impossible.
Author: P. K. Kamthan
Publisher:
Published: 1981
Total Pages: 388
ISBN-13:
DOWNLOAD EBOOK →Topological vector spaces; Sequences spaces; Conservence of series; Further developments in sequences spaces.
Author: Pandelis Dodos
Publisher: Springer Science & Business Media
Published: 2010-05-10
Total Pages: 180
ISBN-13: 3642121527
DOWNLOAD EBOOK →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.