5 papers · 1 filter
Almost preserved extreme points
Ramón J. Aliaga, Luis C. García-Lirola, Juan Guerrero-Viu +2
In this paper we introduce the notion of an almost preserved extreme point (APEP) of a set as a weakening of the concept of preserved extreme points, and we systematically study su…
A covering index for Banach spaces
Matias Raja
We introduce a new isomorphic quantity for Banach spaces, the index , based on finite convex coverings of the unit ball. This index is closely related to the asymptotic moduli…
Representation in by Lipschitz functions
Matias Raja
The isometric universality of the spaces for a non scattered Hausdorff compact does not take into account the ``quality'' of the representation. Indeed, the existence of…
Covering by finitely many convex sets
Matias Raja
Given a finite covering by closed convex sets of , the unit ball of an infinite-dimensional Banach space, we investigate whether there is a set of the covering that contains b…
Compact convex sets that admit a lower semicontinuous strictly convex function
L. García-Lirola, J. Orihuela, M. Raja
We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is emb…