$DW$-compact operators on Banach lattices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917684871954432 |
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| author | Chen, Jin Xi Feng, Jingge |
| author_facet | Chen, Jin Xi Feng, Jingge |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $DW$-compact operators on Banach lattices Chen, Jin Xi Feng, Jingge Functional Analysis Primary 46B42, Secondary 46B50, 47B65 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. |
| title | $DW$-compact operators on Banach lattices |
| topic | Functional Analysis Primary 46B42, Secondary 46B50, 47B65 |
| url | https://arxiv.org/abs/2406.02714 |