ENGLISH

The Volume of Convex Bodies and Banach Space Geometry

By Gilles Pisier

Book information

Publisher
Cambridge University Press
Year
1999
ISBN
052166635X, 9780521666350, 9780521364652, 0521364655, 9780511662454
LCC
QA322.2 .P57 1989
Open Library ID
OL2056942M
Language
english
Format
PDF
Filesize
2 MB (1987349 bytes)
Series
Cambridge tracts in mathematics 94
Pages
267\267
Time added
2010-05-31 15:29:46

Description

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.

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