Gelfand-Phillips-type properties in Banach lattices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908461189562368 |
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| author | Ardakani, Halimeh Miranda, Vinícius C. C. |
| author_facet | Ardakani, Halimeh Miranda, Vinícius C. C. |
| contents | We study $p$-limited and almost $p$-limited sets in Banach lattices and their connections with relatively $p$-compact and relatively compact sets. We investigate the weak and the strong
Gelfand-Phillips property of order $p$, as well as the $p$-GP property introduced by Delgado and Piñeiro, providing conditions under which these properties may coincide. Additionally, we prove that a Banach lattice $E$ is a KB-space if and only if every almost $p$-limited set in $E$ is
relatively weakly compact if and only if every the adjoint of a weakly compact taking values on $E$ is disjoint $p$-summing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gelfand-Phillips-type properties in Banach lattices Ardakani, Halimeh Miranda, Vinícius C. C. Functional Analysis We study $p$-limited and almost $p$-limited sets in Banach lattices and their connections with relatively $p$-compact and relatively compact sets. We investigate the weak and the strong Gelfand-Phillips property of order $p$, as well as the $p$-GP property introduced by Delgado and Piñeiro, providing conditions under which these properties may coincide. Additionally, we prove that a Banach lattice $E$ is a KB-space if and only if every almost $p$-limited set in $E$ is relatively weakly compact if and only if every the adjoint of a weakly compact taking values on $E$ is disjoint $p$-summing. |
| title | Gelfand-Phillips-type properties in Banach lattices |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.16811 |