$DW$-DP operators and $DW$-limited operators on Banach lattices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916502624534528 |
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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 two classes of operators related to disjointly weakly compact sets, which we call $DW$-DP operators and $DW$-limited operators, respectively. They carry disjointly weakly compact subsets of a Banach lattice onto Dunford-Pettis sets and limited sets, respectively. We show that $DW$-DP (resp. $DW$-limited) operators are precisely the operators which are both weak Dunford-Pettis and order Dunford-Pettis (resp. weak$^*$ Dunford-Pettis and order limited) operators. Furthermore, the approximation properties of positive $DW$-DP and positive $DW$-limited operators are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $DW$-DP operators and $DW$-limited operators on Banach lattices Chen, Jin Xi Feng, Jingge Functional Analysis Primary 46B42, Secondary 46B50, 47B65 This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call $DW$-DP operators and $DW$-limited operators, respectively. They carry disjointly weakly compact subsets of a Banach lattice onto Dunford-Pettis sets and limited sets, respectively. We show that $DW$-DP (resp. $DW$-limited) operators are precisely the operators which are both weak Dunford-Pettis and order Dunford-Pettis (resp. weak$^*$ Dunford-Pettis and order limited) operators. Furthermore, the approximation properties of positive $DW$-DP and positive $DW$-limited operators are given. |
| title | $DW$-DP operators and $DW$-limited operators on Banach lattices |
| topic | Functional Analysis Primary 46B42, Secondary 46B50, 47B65 |
| url | https://arxiv.org/abs/2412.01188 |