On dentability and cones with a large dual

On dentability and cones with a large dual

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 C ∗ - C ∗ ¯ = X ∗ ; x is a denting point of a convex set A if and only if x is a point o...

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Veröffentlicht in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2019-07, Vol.113 (3), p.2679-2690
Hauptverfasser: García-Castaño, Fernando, Melguizo Padial, M. A.
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Cones
Continuity
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
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Zusammenfassung: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 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.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-019-00650-3