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

초록

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 $E^{\ast }$ has the order continuous norm and also they are relatively compact if and only if $E^{\ast }$ is discrete with the order continuous norm.

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