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Some results on almost L-weakly and almost M-weakly compact operators. (English) Zbl 07511790

Summary: 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 \(T:E\rightarrow F\) 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.

MSC:

47B60 Linear operators on ordered spaces
47B65 Positive linear operators and order-bounded operators
46B42 Banach lattices
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References:

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