Geometric Aspects of Functional Analysis

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.

Inhalt

The invariant subspace problem on a class of nonreflexive Banach spaces, 1.- Approximational complexity of functions.- Minkowski sums and symmetrizations.- On two theorems of lozanovskii concerning intermediate Banach lattices.- On Milman's inequality and random subspaces which escape through a mesh in ? n .- Isomorphic symmetrization and geometric inequalities.- Dimension, non-linear spectra and width.- Some useful facts about Banach spaces.- Homogeneous Banach spaces.- An approach to pointwise ergodic theorems.- Some remarks on the geometry of convex sets.- On finite dimensional homogeneous Banach spaces.- Vector-valued hausdorff-young inequalities and applications.- Projection bodies.- On a geometric inequality.- A few observations on the connections between local theory and some other fields.