Handbook of the Geometry of Banach Spaces

by W.B. Johnson (Editor), J. Lindenstrauss (Editor)

Overview

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 space theory.

Product Details

ISBN-13:	9780080532806
Publisher:	Elsevier Science
Publication date:	08/15/2001
Series:	ISSN , #1
Sold by:	Barnes & Noble
Format:	eBook
Pages:	1016
File size:	19 MB
Note:	This product may take a few minutes to download.

Table of Contents

Basic concepts in the geometry of Banach spaces (W.B. Johnson, J. Lindenstrauss).

Positive operators (Y.A. Abramovitch, C.D. Aliprantis).

Lp spaces (D. Alspach, E. Odell).

Convex geometry and functional analysis (K. Ball).

A p-sets in analysis: Results, problems and related aspects (J. Bourgain).

Martingales and singular integrals in Banach spaces (D.L. Burkholder).

Approximation properties (P.G. Casazza).

Local operator theory, random matrices and Banach spaces (K.R. Davidson, S.J. Szarek).

Applications to mathematical finance (F. Delbaen).

Perturbed minimization principles and applications (R. Deville, N. Ghoussoub).

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

Special Banach lattices and their applications(S.J. Dilworth).

Some aspects of the invariant subspace problem (P. Enflo,V. Lomonosov).

Special bases in function spaces (T. Figel, P. Wojtaszczyk).

Infinite dimensional convexity (V. Fonf, J. Lindenstrauss, R.R. Phelps).

Uniform algebras as Banach spaces (T.W. Gamelin, S.V. Kisliakov).

Euclidean structure in finite dimensional normed spaces (A.A. Giannopoulos, V.D. Milman).

Renormings of Banach spaces (G. Godefroy).

Finite dimensional subspaces of Lp (W.B. Johnson, G. Schechtman).

Banach spaces and classical harmonic analysis (S.V. Kisliakov).

Aspects of the isometric theory of Banach spaces (A. Koldobsky, H. Konig).

Eigenvalues of operators and applications (H. Konig).

Editorial Reviews

"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.

From the Publisher