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.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
