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Koethe-Bochner Function Spaces : Progress in Mathematics - Pei-Kee Lin

Koethe-Bochner Function Spaces

Progress in Mathematics

Hardcover Published: 12th December 2003
ISBN: 9780817635213
Number Of Pages: 370

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This monograph is devoted to the study of KAthea "Bochner function spaces, an area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. It presents a comprehensive view of KAthea "Bochner function spaces, from the subjecta (TM)s origins in functional analysis to its connections to other disciplines.

Key topics and features:

a Considerable background material provided, including a compilation of important theorems and concepts in classical functional analysis, as well as a discussion of the Dunforda "Pettis Property, tensor products of Banach spaces, relevant geometry, and the basic theory of conditional expectations and martingales

a Rigorous treatment of KAthea "Bochner spaces, encompassing convexity, measurability, stability properties, Dunforda "Pettis operators, and Talagrand spaces, with a particular emphasis on open problems

a Detailed examination of Talagranda (TM)s Theorem, Bourgaina (TM)s Theorem, and the Diaza "Kalton Theorem, the latter extended to arbitrary measure spaces

a "Notes and remarks" after each chapter, with extensive historical information, references, and questions for further study

a Instructive examples and many exercises throughout

Both expansive and precise, this booka (TM)s unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

From the reviews: "This book is a nice and useful reference for researchers in functional analysis who wish to have a quite comprehensive survey of geometric properties of Banach spaces of vector-valued functions." ---Mathematical Reviews "This book ! gives in fact an exhaustive and very up-to-date account of several aspects of the general theory (isomorphic) and geometry of Banach spaces. This book is self-contained with an exhaustive list of references at the end of each chapter. Apart from well thought-out exercises at the end of each section, the 'Notes and Remarks' section at the end of each chapter contains several open questions with additional comments and references. This book is worth having on the shelves of anyone interested in Banach space theory. I thoroughly enjoyed going through it."(ZENTRALBLATT MATH) "This book, though somewahte restrictively entitled, gives in fact an exhaustive and very up-to-date account of several aspects of the general theory (isomorphic) and geometry of Banach spaces... This book is self-contained with an exhaustive list of references at the end of each chapter. Apart from well thoght-out exervises at the end of each section,t he 'Notes and Remarks' section at the end of each chapter contains several open questions with additional somments and references. This book is worth having on the shelves of anyone interested in Banach space theory. I thoroughly enjoyed going through it." ---Zenteralblatt MATH

Preface
Notation
Classical Theoremsp. 1
Convexity and Smoothnessp. 101
Kothe - Bochner Function Spacesp. 143
Stability Properties Ip. 219
Stability Properties IIp. 247
Continuous Function Spacesp. 313
Indexp. 367
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780817635213
ISBN-10: 0817635211
Series: Progress in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 370
Published: 12th December 2003
Publisher: BIRKHAUSER BOSTON INC
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.59