Handbook of the Geometry of Banach Spaces

Couverture
Elsevier, 15 août 2001 - 1016 pages

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.

 

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Table des matières

Chapter 2 Positive operators
85
Chapter 3 Lp spaces
123
Chapter 4 Convex geometry and functional analysis
161
Results problems and related aspects
195
Chapter 6 Martingales and singular integrals in Banach spaces
233
Chapter 7 Approximation properties
271
Chapter 8 Local operator theory random matrices and Banach spaces
317
Chapter 9 Applications to mathematical finance
367
Chapter 14 Special bases in function spaces
561
Chapter 15 Infinite dimensional convexity
599
Chapter 16 Uniform algebras as Banach spaces
671
Chapter 17 Euclidean structure in finite dimensional normed spaces
707
Chapter 18 Renormings of Banach spaces
781
Chapter 19 Finite dimensional subspaces of Lp
837
Chapter 20 Banach spaces and classical harmonic analysis
871
Chapter 21 Aspects of the isometric theory of Banach spaces
899

Chapter 10 Perturbed minimization principles and applications
393
Chapter 11 Operator ideals
437
Chapter 12 Special Banach lattices and their applications
497
Chapter 13 Some aspects of the invariant subspace problem
533
Chapter 22 Eigenvalues of operators and applications
941
Author Index
975
Subject Index
993
Droits d'auteur

Expressions et termes fréquents

Informations bibliographiques