DW$-compact operators on Banach lattices
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 appl...
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| creator | Chen, Jin Xi Feng, Jingge |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2406.02714 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.2406.02714</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Functional Analysis |
| title | DW$-compact operators on Banach lattices |
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