Continuous images of weakly compact subsets of Banach spaces

Yoav Benyamini, Mary Ellen Rudin and Michael L. Wage

Vol. 70 (1977), No. 2, 309–324

DOI: 10.2140/pjm.1977.70.309

Abstract

We give a positive answer to a problem of Lindenstrauss by showing that the family of compact Hausdorff spaces which are homeomorphic to weakly compact subsets of Banach spaces (Eberlein compacts) is stable under continuous images. This is equivalent to the fact that a Banach space E is a subspace of a WCG space iff the unit ball of E^∗ is an Eberlein compact when equipped with the w^∗-topology. We also study some topological properties of Eberlein compacts.

Mathematical Subject Classification

Primary: 46B05, 46B05

Milestones

Received: 15 September 1976

Published: 1 June 1977