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On dentability and cones with a large dual

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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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Acknowledgements

We thank the referees for their suggestions which have helped us to improve the overall aspect of the manuscript.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Escuela Politécnica Superior, Universidad de Alicante, San Vicente del Raspeig, 03080, Alicante, Spain

    Fernando García-Castaño & M. A. Melguizo Padial

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  1. Fernando García-Castaño
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  2. M. A. Melguizo Padial
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Correspondence to Fernando García-Castaño.

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M. A. Melguizo Padial has been supported by project MTM2017-86182-P (AEI/FEDER, UE). Fernando García-Castaño has been partially supported by MINECO and FEDER (MTM2014-54182), by Fundación Séneca—Región de Murcia (19275/PI/14), and by MTM2017-86182-P (AEI/FEDER, UE).

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García-Castaño, F., Melguizo Padial, M.A. On dentability and cones with a large dual. RACSAM 113, 2679–2690 (2019). https://doi.org/10.1007/s13398-019-00650-3

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