Handbook of the Geometry of Banach Spaces: Volume 2

ISBN-13: 9780444513052 / Angielski / Twarda / 2003 / 870 str.

Unknown; W. B. Johnson; J. Lindenstrauss

Opis

Presenting an overview of most aspects of modern Banach space theory and its applications, this handbook offers up-to-date surveys by a range of expert authors. 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. contains all the background needed for reading any other chapter. Each of the 21 articles after his 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. 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. The handbook should be useful to researchers in Banach theory, as well as graduate students and mathematicians who want to get an idea of the various developments in Banach space theory.

Recenzje

"The editors, Bill Johnson and Joram Lindenstrauss have continued the steady hand they applied to the first volume to this second and final part of the Handbook (....) it is clear that these two volumes will become a standard and important reference for both graduate students and more experienced Banach space researchers. The Handbook is a must for any serious mathematics library and highly recommended for researchers in this and neighbouring fields." --Ian Doust - University of New South Wales. The Australian Mathematical Society Gazette. 2004.

Spis treści

Preface.

Descriptive Set Theory and Banach Spaces (S.A. Argyros, G. Godefroy, H.P. Rosenthal).

Ramsey Methods in Banach Spaces (W.T. Gowers).

Quasi-Banach Spaces (N. Kalton).

Interpolation of Banach Spaces (N. Kalton, S. Montgomery-Smith).

Probabilistic Limit Theorems in the Setting of Banach Spaces (M. Ledoux, J. Zinn).

Quotients of Finite-Dimensional Banach Spaces; Random Phenomena (P. Mankiewicz, N. Tomczak-Jaegermann).

Banach Spaces with few Operators (B. Maurey).

Type-cotype and K-convexity (B. Maurey).

Distortion and Asymptotic Structure (E. Odell, T. Schlumprecht).

Sobolev Spaces (A. Pelczynski, M. Wojciechowski).

Operator Spaces (G. Pisier).

Non-commutative Lp-spaces (G. Pisier, Q. Xu).

Geometric Measure Theory in Banach Spaces (D. Preiss).

The Banach Spaces C (K).

Concentration, Results and Applications (G. Schechtman).

Uniqueness of Structure in Banach Spaces (L. Tzafriri).

Spaces of Analytic Functions with Integral Norm (P. Wojtaszczyk).

Extension of Bounded Linear Operators (M. Zippin).

Nonseparable Banach Spaces (V. Zizler).

Addenda and Corrigenda to Chapter 7, Approximation Properties by Peter G. Cassazza).

Addenda and Corrigenda to Chapter 8, Local Operator Theory, Random Matrices and Banach Spaces (K.R. Davidson, S.J. Szarek).

Operator Ideals (J. Diestel, H. Jarchow, A. Pietsch).

Addenda and Corrigenda to Chapter 15, Infinite Dimensional Convexity).