The Volume of Convex Bodies and Banach Space Geometry
By (author) Gilles Pisier
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Volume of Convex Bodies and Banach Space Geometry by Gilles Pisier
Book DescriptionThis 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.
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Book DetailsISBN: 9780521666350
(228mm x 152mm x 15mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 27-May-1999
Country of Publication: United Kingdom
Books By Author Gilles Pisier
Martingales in Banach Spaces, Hardback (June 2016)
This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Introduction to Operator Space Theory, Paperback (August 2003)» View all books by Gilles Pisier
An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
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