RELATIONSHIP BETWEEN DIFFERENT CLASSES OF SETS IN THE DUAL OF BANACH LATTICES

Abstract

. This paper focuses on different classes of sets in the dual of a Banach lattice such as V-sets, L-sets, Right sets, L-limited sets and almost L-sets and then, based on the connections between them, some operator characterizations are obtained. As a result, we show that each almost L-set and Right set is a V-set and a V-set is itself an L-limited set. In particular, it is proved that almost L-sets are relatively weakly compact if and only if E & lowast; has the order continuous norm and also they are relatively compact if and only if E & lowast; is discrete with the order continuous norm.