Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 1987–88

Yaki Sternfeld (auth.), Joram Lindenstrauss, Vitali D. Milman (eds.)9780387513034, 0-387-51303-5

This is the third published volume of the proceedings of the Israel Seminar on Geometric Aspects of Functional Analysis. The large majority of the papers in this volume are original research papers. There was last year a strong emphasis on classical finite-dimensional convexity theory and its connection with Banach space theory. In recent years, it has become evident that the notions and results of the local theory of Banach spaces are useful in solving classical questions in convexity theory. The present volume contributes to clarifying this point. In addition this volume contains basic contributions to ergodic theory, invariant subspace theory and qualitative differential geometry.

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Table of contents :
Hilbert’s 13th problem and dimension….Pages 1-49
On the duality problem for entropy numbers of operators….Pages 50-63
Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n -dimensional space….Pages 64-104
An “isomorphic” version of the sauer-shelah lemma and the banach-mazur distance to the cube….Pages 105-112
On complemented subspaces of H 1 and VMO ….Pages 113-125
An approximation theorem for vector valued functions….Pages 126-137
Geometry of finite dimensional subspaces and quotients of L p ….Pages 138-175
Estimates of bernstein widths of sobolev spaces….Pages 176-185
Probabilistic proofs of existence of rare events….Pages 186-201
On the behavior of the constant in the littlewood-paley inequality….Pages 202-208
On kolmogorov’s rearrangement problem for orthogonal systems and garsia’s conjecture….Pages 209-250
Volumes of sections of cubes and related problems….Pages 251-260
On santaló’s inequality….Pages 261-263
Estimates related to steiner symmetrizations….Pages 264-273
A remark concerning the dependence on ɛ in dvoretzky’s theorem….Pages 274-277
Almost euclidean sections in spaces with a symmetric basis….Pages 278-288