DW-compact operators on Banach lattices

2024/06/04 by Jin Xi Chen, Chen, Jin Xi, Jingge Feng +1 · 1 citation
Mathematics · #47B65 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B42 #Secondary 46B50

paper · pdf · doi:10.48550/arxiv.2406.02714

openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• On the duality of DW-compact operators and DW-DP operators

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