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The Volume of Convex Bodies and Banach Space Geometry (Cambridge Tracts in Mathematics, Series Number 94),Used
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Now in paperback, this popular book gives a selfcontained presentation of a number of recent results, which relate the volume of convex bodies in ndimensional Euclidean space and the geometry of the corresponding finitedimensional 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 selfcontained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse BrunnMinkowski 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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