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K¶the-Bochner Function Spaces : Progress in Mathematics - Pei-Kee Lin

K¶the-Bochner Function Spaces

By: Pei-Kee Lin

Hardcover | 13 January 2004

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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.

Industry Reviews
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

You Can Find This Book In

Non-FictionMathematicsCalculus & Mathematical AnalysisFunctional Analysis & TransformsProbability & Statistics

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