Sequences And Series In Banach Spaces

Author : J. Diestel
Publisher : Springer Science & Business Media
ISBN 13 : 1461252008
Total Pages : 273 pages
Book Rating : 4.09/5 ( download)

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Download or read book Sequences and Series in Banach Spaces written by J. Diestel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9783540908593
Total Pages : 261 pages
Book Rating : 4.95/5 ( download)

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Download or read book Sequences and Series in Banach Spaces written by Joseph Diestel and published by . This book was released on 1984-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vladimir Kadets
Publisher : Birkhäuser
ISBN 13 : 3034891962
Total Pages : 162 pages
Book Rating : 4.67/5 ( download)

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Download or read book Series in Banach Spaces written by Vladimir Kadets and published by Birkhäuser. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9780824787233
Total Pages : 234 pages
Book Rating : 4.34/5 ( download)

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Download or read book Classical Sequences in Banach SPates written by Sylvia Guerre-Delabriere and published by CRC Press. This book was released on 1992-07-21 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Pawan K. Jain
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9788173192395
Total Pages : 162 pages
Book Rating : 4.91/5 ( download)

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Download or read book Sequence Spaces and Applications written by Pawan K. Jain and published by Alpha Science Int'l Ltd.. This book was released on 1999 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3642665578
Total Pages : 202 pages
Book Rating : 4.78/5 ( download)

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Download or read book Classical Banach Spaces I written by J. Lindenstrauss and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : S. A. Mohiuddine
Publisher : CRC Press
ISBN 13 : 100061008X
Total Pages : 530 pages
Book Rating : 4.86/5 ( download)

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Download or read book Sequence Space Theory with Applications written by S. A. Mohiuddine and published by CRC Press. This book was released on 2022-07-20 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications. Features Discusses the Fibonacci and vector valued difference sequence spaces Presents the solution of Volterra integral equation in Banach algebra Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix Presents the Tauberian theorems of double sequences Discusses the paranormed Riesz difference sequence space of fractional order Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.

Author : P. K. Kamthan
Publisher :
ISBN 13 :
Total Pages : 388 pages
Book Rating : 4.35/5 ( download)

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Download or read book Sequence Spaces and Series written by P. K. Kamthan and published by . This book was released on 1981 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological vector spaces; Sequences spaces; Conservence of series; Further developments in sequences spaces.

Author : Pandelis Dodos
Publisher : Springer Science & Business Media
ISBN 13 : 3642121527
Total Pages : 180 pages
Book Rating : 4.24/5 ( download)

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Download or read book Banach Spaces and Descriptive Set Theory: Selected Topics written by Pandelis Dodos and published by Springer Science & Business Media. This book was released on 2010-05-10 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Mohammad Mursaleen
Publisher : CRC Press
ISBN 13 : 1000045153
Total Pages : 313 pages
Book Rating : 4.54/5 ( download)

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Download or read book Sequence Spaces written by Mohammad Mursaleen and published by CRC Press. This book was released on 2020-03-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.