On Localized Weak Precompactness in Banach Spaces

Abstract

In this paper we make a study of K-weakly precompact sets A in Banach spaces. We give various characterizations of such sets by the effective use of the lifting theory, weak*-–A*-dentability and a K-valued weak*-measurable function constructed in the case where A is non-K-weakly precompact. These results also can be regarded as generalizations of corresponding ones on Pettis sets and weakly precompact sets.