Reciprocal Dunford--Pettis sets and V$^*$-sets in Banach lattices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909223966736384 |
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| author | Chen, Jin Xi Li, Xi |
| author_facet | Chen, Jin Xi Li, Xi |
| contents | In this short note, we show that one cannot differentiate between reciprocal Dunford--Pettis sets and V$^*$-sets in a Banach lattice. That is, for a bounded subset $K$ of a Banach lattice $E$, $K$ is a V$^*$-set if and only if $K$ is a reciprocal Dunford--Pettis set, or equivalently, if and only if every disjoint sequence in the solid hull of $K$ is weakly null (i.e. $K$ is disjointly weakly compact). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_09853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reciprocal Dunford--Pettis sets and V$^*$-sets in Banach lattices Chen, Jin Xi Li, Xi Functional Analysis Primary 46B42, Secondary 46B50, 47B65 In this short note, we show that one cannot differentiate between reciprocal Dunford--Pettis sets and V$^*$-sets in a Banach lattice. That is, for a bounded subset $K$ of a Banach lattice $E$, $K$ is a V$^*$-set if and only if $K$ is a reciprocal Dunford--Pettis set, or equivalently, if and only if every disjoint sequence in the solid hull of $K$ is weakly null (i.e. $K$ is disjointly weakly compact). |
| title | Reciprocal Dunford--Pettis sets and V$^*$-sets in Banach lattices |
| topic | Functional Analysis Primary 46B42, Secondary 46B50, 47B65 |
| url | https://arxiv.org/abs/2406.09853 |