DW-compact operators on Banach lattices

This paper is devoted to the study of DW-compact operators, that is, those operators which map disjointly weakly compact sets in a Banach lattice onto relatively compact sets. We show that DW-compact operators are precisely the operators which are both Dunford–Pettis and AM-compact. As an application, Banach lattices with the property that every disjointly weakly compact set is a limited (resp. Dunford–Pettis) set, are characterized by using DW-compact operators.