Data di Pubblicazione:
2009
Citazione:
Convex sets without diametral pairs / L. Vesely. - In: EXTRACTA MATHEMATICAE. - ISSN 0213-8743. - 24:3(2009), pp. 271-280.
Abstract:
Let X be an infinite dimensional normed linear space. It is not difficult
to see that arbitrarily near (in the Hausdorff metric) to the unit ball of
X there exists a nonempty closed convex set whose
diameter is not attained. We show that such sets are dense in
the metric space of all nonempty bounded closed convex subsets of X
if and only if either X is not a
reflexive Banach space or X is a reflexive Banach space in which every
weakly closed set contained in the unit sphere S_X has empty relative
interior in S_X.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Diametral pair ; bounded closed convex set ; Hausdorff metric
Elenco autori:
L. Vesely
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