Some results on almost L-weakly and almost M-weakly compact operators

The class of weakly compact operators does not contain that of almost L-weakly compact operators. In this paper, we provide a complete answer by giving necessary and sufficient conditions for which every positive almost L-weakly compact operator T : E -> F between two Banach lattices is weakly compact. On the other hand, we investigate conditions under which the adjoint operator of every positive almost L-weakly compact operator is almost M-weakly compact.

Automated summary

In this paper, we investigate the relationship between weakly compact operators and almost L-weakly compact operators. We provide necessary and sufficient conditions for which every positive almost L-weakly compact operator T : E -> F is weakly compact, and we also study the conditions under which the adjoint operator of every positive almost L-weakly compact operator is almost M-weakly compact.