L-LIMITED AND ALMOST L-LIMITED SETS IN DUAL BANACH LATTICES

Abstract

Following the concept of L-limited sets in dual Banach spaces

introduced by Salimi and Moshtaghioun, we introduce the concept of almost

L-limited sets in dual Banach lattices and then by a class of operators on

Banach lattices, so called disjoint limited completely continuous operators, we

characterize Banach lattices in which almost L-limited subsets of their dual,

coincide with L-limited sets.