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The Volume of Convex Bodies and Banach Space Geometry : Cambridge Tracts in Mathematics (Paperback) - Gilles Pisier

The Volume of Convex Bodies and Banach Space Geometry

Cambridge Tracts in Mathematics (Paperback)

Paperback

Published: 26th July 1999
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Now in paperback, this popular book gives a self-contained presentation of a number of recent results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory, and the local theory of Banach spaces. The first part of the book presents self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality. In the second part Pisier gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). This text will be a superb choice for courses in analysis and probability theory.

."..makes more accessible many important recent results from the theory of convex sets and the local theory of Banach spaces." Mathematical Reviews

Introduction
Notation and preliminary background
Gaussian variable, K-convexity
Ellipsoids
Dvoretzky's theorem
Entropy, approximation numbers, and Gaussian processes
Volume ratio
Milman's ellipsoids
Another proof of the QS theorem
Volume numbers
Weak cotype 2
Weak type 2
Weak Hilbert spaces
Some examples: the Tsirelson spaces
Reflexivity of weak Hilbert spaces
Fredholm determinants
Final remarks
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521666350
ISBN-10: 052166635X
Series: Cambridge Tracts in Mathematics (Paperback)
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 268
Published: 26th July 1999
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.96 x 15.49  x 1.65
Weight (kg): 0.39