Handbook of the Geometry of Banach Spaces: Volume 1

W. B. Johnson

The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations.The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers.As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach

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Table of contents :
books_005……Page 1
books_004……Page 2
books_003……Page 3
books_002……Page 4
1……Page 5
2……Page 7
3……Page 8
4……Page 92
5……Page 130
6……Page 167
7……Page 201
8……Page 239
9……Page 276
10……Page 322
11……Page 372
12……Page 397
13……Page 440
14……Page 500
15……Page 536
16……Page 563
17……Page 600
18……Page 672
19……Page 708
20……Page 781
21……Page 836
22……Page 870
23……Page 898
24……Page 939
25……Page 973
26……Page 990