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Banach Spaces of Continuous Functions as Dual Spaces

Author : H. G. Dales

Publisher : Springer

Page : 286 pages

File Size : 43,34 MB

Release : 2016-12-13

Category : Mathematics

ISBN : 3319323490

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Book Description

This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.







Function Spaces

Author : Krzysztof Jarov

Publisher : CRC Press

Page : 450 pages

File Size : 21,15 MB

Release : 2020-08-27

Category : Mathematics

ISBN : 1000147932

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Book Description

This book is based on the conference on Function Spaces held at Southern Illinois University at Edwardsville, in April, 1990. It is designed to cover a wide range of topics, including spaces of analytic functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.



Classical Banach Spaces

Author : Joram Lindenstrauss

Publisher : Springer

Page : 254 pages

File Size : 42,98 MB

Release : 2006-11-15

Category : Mathematics

ISBN : 3540377328

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Book Description

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.



Smooth Analysis in Banach Spaces

Author : Petr Hájek

Publisher : Walter de Gruyter GmbH & Co KG

Page : 514 pages

File Size : 42,92 MB

Release : 2014-10-29

Category : Mathematics

ISBN : 3110258994

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Book Description

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.



Banach Spaces of Vector-Valued Functions

Author : Pilar Cembranos

Publisher : Springer

Page : 124 pages

File Size : 41,21 MB

Release : 2006-11-14

Category : Mathematics

ISBN : 3540696393

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Book Description

"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.





Isometries on Banach Spaces

Author : Richard J. Fleming

Publisher : CRC Press

Page : 209 pages

File Size : 33,17 MB

Release : 2002-12-23

Category : Mathematics

ISBN : 1420026151

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Book Description

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



History of Banach Spaces and Linear Operators

Author : Albrecht Pietsch

Publisher : Springer Science & Business Media

Page : 877 pages

File Size : 10,4 MB

Release : 2007-12-31

Category : Mathematics

ISBN : 0817645969

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Book Description

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.