$DW$-L-Weakly Compact Operators Between Banach Lattices

In this paper we introduce a class of operators which we call $DW$-L-weakly compact operators. They carry disjointly weakly compact subsets of a Banach lattice onto L-weakly compact sets. The class of $DW$-L-weakly compact operators is closely related to two recently introduced classes of operators: almost L-weakly compact operators and order L-weakly compact operators. We show that $DW$-L-weakly compact operators are precisely those operators which are both almost L-weakly compact and order L-weakly compact. The adjoint and the order structure of $DW$-L-weakly compact operators are also considered.