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arXiv · 2401.10102

On dentability and cones with a large dual

Fernando García-Castaño·M. A. Melguizo Padial
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Abstract

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.

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BibTeXRIS

Fernando García-Castaño, M. A. Melguizo Padial. 2024-01-15. On dentability and cones with a large dual. https://doi.org/10.1007/s13398-019-00650-3

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