Topics in Banach Space Theory, Volume 10

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Taylor & Francis, Jan 4, 2006 - Mathematics - 373 pages
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This book grew out of a one-semester course given by the second author in 2001 and a subsequent two-semester course in 2004-2005, both at the Univ- sity of Missouri-Columbia. The text is intended for a graduate student who has already had a basic introduction to functional analysis; the aim is to give a reasonably brief and self-contained introduction to classical Banach space theory. Banach space theory has advanced dramatically in the last 50 years and webelievethatthetechniquesthathavebeendevelopedareverypowerfuland should be widely disseminated amongst analysts in general and not restricted to a small group of specialists. Therefore we hope that this book will also prove of interest to an audience who may not wish to pursue research in this area but still would like to understand what is known about the structure of the classical spaces. Classical Banach space theory developed as an attempt to answer very natural questions on the structure of Banach spaces; many of these questions date back to the work of Banach and his school in Lvov. It enjoyed, perhaps, its golden period between 1950 and 1980, culminating in the de?nitive books by Lindenstrauss and Tzafriri [138] and [139], in 1977 and 1979 respectively. The subject is still very much alive but the reader will see that much of the basic groundwork was done in this period.
  

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Contents

Bases and Basic Sequences
1
The Classical Sequence Spaces
29
Special Types of Bases
51
Banach Spaces of Continuous Functions
73
The LpSpaces for 1 p oo
125
Factorization Theory
165
Absolutely Summing Operators
195
Perfectly Homogeneous Bases and Their Applications
221
An Introduction to Local Theory
289
Important Examples of Banach Spaces
309
A Fundamental Notions
327
С Main Features of FiniteDimensional Spaces
335
E Convex Sets and Extreme Points
341
G Weak Compactness of Sets and Operators
347
References
353
Index
365

pSubspaces of Banach Spaces
247
Finite Representability of pSpaces
263

Common terms and phrases

References to this book

Funktionalanalysis
Dirk Werner
No preview available - 2007
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