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  3. The Volume of Convex Bodies and Banach Space Geometry
  • Cited by 382
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
1989
Online ISBN:
9780511662454
DOI:
https://doi.org/10.1017/CBO9780511662454
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
Series:
Cambridge Tracts in Mathematics (94)
Information

Book 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.

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