Handbook of the Geometry of Banach Spaces : Volume 2

W B Johnson

ISBN 10: 0444513051 / ISBN 13: 9780444513052

Editore: Elsevier Science, 2003

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Codice articolo 9780444513052

Dati bibliografici

• Titolo: Handbook of the Geometry of Banach Spaces : Volume 2
• Editore: Elsevier Science
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 0444513051
• ISBN 13: 9780444513052
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 170 A x 51 P (millimetri) 241 millimetri di larghezza per 170 millimetri di altezza per 51 millimetri di profondità
• Peso: 1497 grammi

Descrizione articolo

Riassunto

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.

Recensione

"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.