On dentability and cones with a large dual
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929214605754368 |
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| author | García-Castaño, Fernando Padial, M. A. Melguizo |
| author_facet | García-Castaño, Fernando Padial, M. A. Melguizo |
| contents | In this paper, we provide some equivalences on dentability in normed spaces. Among others we prove: the origin is a denting point of a pointed cone $C$ if and only if it is a point of continuity for such a cone and $\overline{C^*-C^*}=X^*$; $x$ is a denting point of a convex set $A$ if and only if $x$ is a point of continuity and a weakly strongly extreme point of $A$. We also analize how our results help us to shed some light on several open problems in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On dentability and cones with a large dual García-Castaño, Fernando Padial, M. A. Melguizo Functional Analysis 46B40, 46A40, 46B20 In this paper, we provide some equivalences on dentability in normed spaces. Among others we prove: the origin is a denting point of a pointed cone $C$ if and only if it is a point of continuity for such a cone and $\overline{C^*-C^*}=X^*$; $x$ is a denting point of a convex set $A$ if and only if $x$ is a point of continuity and a weakly strongly extreme point of $A$. We also analize how our results help us to shed some light on several open problems in the literature. |
| title | On dentability and cones with a large dual |
| topic | Functional Analysis 46B40, 46A40, 46B20 |
| url | https://arxiv.org/abs/2401.10102 |