DW-DP operators and DW-limited operators on Banach lattices

Abstract

This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call DW-DP operators and DW-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that DW-DP (resp. DW-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak\(^*\) Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive DW-DP and positive DW-limited operators are given.