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Klappentext DESCRIPTION: The aim of this Handbook is to present an overview of the main research directions and results in Banach space theory obtained during the last half century. The scope of the theory! having widened considerably over the years! now has deep and close ties with many areas of mathematics! including harmonic analysis! complex analysis! partial differential equations! classical convexity! probability theory! combinatorics! logic! approximation theory! geometric measure theory! operator theory! and others. In choosing a topic for an article in the Handbook we considered both the interest the topic would have for non specialists as well as the importance of the topic for the core of Banach space theory! which is the study of the geometry of infinite dimensional Banach spaces and n-dimensional normed spaces within finite but large (local theory). TABLE OF CONTENTS: Preface; Descriptive Set Theory and Banach Spaces; Ramsey Methods in Banach Spaces; Quasi-Banach Spaces; Interpolation of Banach Spaces; Probabilistic Limit Theorems in the Setting of Banach Spaces; Quotients of Finite-Dimensional Banach Spaces; Random Phenomena; Banach Spaces with few Operators; Type-cotype and K- convexity; Distortion and Asymptotic Structure; Sobolev Spaces; Operator Spaces; Non-commutative Lp-spaces; Geometric Measure Theory in Banach Spaces; The Banach Spaces; Concentration! Results and Applications; Uniqueness of Structure in Banach Spaces; Spaces of Analytic Functions with Integral Norm; Extension of Bounded Linear Operators; Nonseparable Banach Spaces Zusammenfassung Encouraged by new perspectives in Banach space theory! the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications. Inhaltsverzeichnis 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). ...
List of contents
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).
Report
"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.
