Let K be a nonempty closed convex subset of a real Banach space of dimension at least two. Suppose that K does not contain any hyperplane. Then the set of all support points of K is pathwise connected and the set Σ1(K) of all norm-one support functionals of K is uncountable. This was proved for bounded K by L. Veselý and the author [3], and for general K by L. Veselý [8] using a parametric smooth variational principle. We present an alternative geometric proof of the general case in the spirit of [3]. © Heldermann Verlag.

On support points and functionals of unbounded convex sets / C.A. DE BERNARDI. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 20:3(2013), pp. 871-880.

On support points and functionals of unbounded convex sets

C.A. DE BERNARDI
2013

Abstract

Let K be a nonempty closed convex subset of a real Banach space of dimension at least two. Suppose that K does not contain any hyperplane. Then the set of all support points of K is pathwise connected and the set Σ1(K) of all norm-one support functionals of K is uncountable. This was proved for bounded K by L. Veselý and the author [3], and for general K by L. Veselý [8] using a parametric smooth variational principle. We present an alternative geometric proof of the general case in the spirit of [3]. © Heldermann Verlag.
Bishop-phelps theorem; Convex set; Support functional; Support point
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/251005
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