Compactness in B(X)

Abstract

This paper is concerned with compactness for some topologies on the collection of bounded linear operators on Banach spaces. New versions of the Eberlein-Smulian theorem and Day's lemma in the collection are established. Also we obtain a partial solution of the dual problem for the quasi approximation property, that is, it is shown that for a Banach space X if X** is separable and X* has the quasi approximation property, then X has the quasi approximation property. (C) 2005 Elsevier Inc. All rights reserved.