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The Volume of Convex Bodies and Banach Space Geometry (Cambridge Tracts in Mathematics, Series Number 94)

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The Volume of Convex Bodies and Banach Space Geometry (Cambridge Tracts in Mathematics, Series Number 94) image
ISBN-10:

0521364655

ISBN-13:

9780521364652

Author(s): Pisier, Gilles
Released: Nov 24, 1989
Publisher: Cambridge University Press
Format: Hardcover, 274 pages
Related ISBN: 9780521666350
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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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