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 , and for general K by L. Veselý  using a parametric smooth variational principle. We present an alternative geometric proof of the general case in the spirit of . © 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.
|Titolo:||On support points and functionals of unbounded convex sets|
|Parole Chiave:||Bishop-phelps theorem; Convex set; Support functional; Support point|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2013|
|Appare nelle tipologie:||01 - Articolo su periodico|