Methods in Banach Space Theory

✍ Scribed by Jesus M. F. Castillo, William B. Johnson

• Publisher: Cambridge University Press
• Year: 2006
• Tongue: English
• Leaves: 371
• Series: London Mathematical Society Lecture Note Series
• Category: Library

✦ Synopsis

This book presents an overview of modern Banach space theory. It contains sixteen papers that reflect the wide expanse of the subject. Articles are gathered into five sections according to methodology rather than the topics considered. The sections are: geometrical methods; homological methods; topological methods; operator theoretic methods; and also function space methods. Each section contains survey and research papers describing the state-of-the-art in the topic considered as well as some of the latest most important results. Researchers working in Banach space theory, functional analysis or operator theory will find much of interest here.

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 8
Acknowledgements......Page 10
Picture: closing at the main lecture room......Page 12
Saturated extensions, the attractors method and Hereditarily James Tree Spaces......Page 14
The Daugavet property for Lindenstrauss spaces......Page 104
Weakly null sequences in the Banach space C(K)......Page 110
Yet another proof of Sobczyk's theorem......Page 146
The category of exact sequences of Banach spaces......Page 152
Extension problems for C(K) spaces and twisted sums......Page 172
Palamodov's questions from Homological methods in the theory of locally convex spaces......Page 182
Ordinal representability in Banach spaces......Page 196
Overclasses of the class of Radon-Nikodym compact spaces......Page 210
Convexity, compactness and distances......Page 228
Weyl's and Browder's theorems through the quasi-nilpotent part of an operator......Page 252
Multiplications and elementary operators in the Banach space setting......Page 266
Interpolation of Banach Spaces by the \gamma -method......Page 306
Solvability of an integral equation in BC(R+)......Page 320
Harald Bohr meets Stefan Banach......Page 330
Selected problems on the structure of complemented subspaces of Banach spaces......Page 354
List of participants......Page 368
Picture: some like it fun......Page 371