The volume of convex bodies and Banach space geometry

Description

This book aims to give a self-contained presentation of a number of 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 book is in two parts. The first presents self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality. The second part 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). The book is based on courses given in Paris and in Texas.

First Sentence

Let, E, F be Banach spaces.

Subjects

Series Statement

• Cambridge tracts in mathematics ;

Other Editions

• The volume of convex bodies and Banach space geometryCambridge University Press1989-01-01
• The Volume of Convex Bodies and Banach Space GeometryPaperbackCambridge University Press1999-08-01