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  3. The Volume of Convex Bodies and Banach Space Geometry
  • Cited by 400
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2010
      October 1989
      ISBN:
      9780511662454
      9780521666350
      DOI:
      https://doi.org/10.1017/CBO9780511662454
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.365kg, 268 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
      Series:
      Cambridge Tracts in Mathematics (94)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
    Series:
    Cambridge Tracts in Mathematics (94)
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    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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