4.2 Article

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

Journal

POSITIVITY
Volume 26, Issue 2, Pages -

Publisher

SPRINGER
DOI: 10.1007/s11117-022-00911-3

Keywords

Almost L-weakly compact operator; Almost M-weakly compact operator; Weakly compact operator; Banach lattice; Order continuous norm; KB-space

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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.
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.

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