  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.
