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arXiv · 2406.02714

$DW$-compact operators on Banach lattices

Jin Xi Chen·Jingge Feng
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Abstract

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.

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Jin Xi Chen, Jingge Feng. 2024-06-04. $DW$-compact operators on Banach lattices. https://arxiv.org/abs/2406.02714

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