Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 1986–87

C. J. Read (auth.), Joram Lindenstrauss, Vitali D. Milman (eds.)9780387193533, 0-387-19353-7

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 :
The invariant subspace problem on a class of nonreflexive Banach spaces, 1….Pages 1-20
Approximational complexity of functions….Pages 21-43
Minkowski sums and symmetrizations….Pages 44-66
On two theorems of lozanovskii concerning intermediate Banach lattices….Pages 67-83
On Milman’s inequality and random subspaces which escape through a mesh in ℝ n ….Pages 84-106
Isomorphic symmetrization and geometric inequalities….Pages 107-131
Dimension, non-linear spectra and width….Pages 132-184
Some useful facts about Banach spaces….Pages 185-200
Homogeneous Banach spaces….Pages 201-203
An approach to pointwise ergodic theorems….Pages 204-223
Some remarks on the geometry of convex sets….Pages 224-231
On finite dimensional homogeneous Banach spaces….Pages 232-238
Vector-valued hausdorff-young inequalities and applications….Pages 239-249
Projection bodies….Pages 250-270
On a geometric inequality….Pages 271-282
A few observations on the connections between local theory and some other fields….Pages 283-289