3 citations · 3 across the 5 of their papers we have counts for
7 papers
Polyhedral normed spaces: the structural theorem and locally finite tilings
Carlo Alberto De Bernardi, Helena del Rìo, Tommaso Russo +1
A fundamental result due to Fonf (1981) asserts that the unit sphere of every polyhedral Banach space is covered by true faces of the unit ball. The principal aim of our paper is t…
ABB theorems: Results and limitations in infinite dimensions
Aris Daniilidis, Carlo de Bernardi, Enrico Miglierina
We construct a weakly compact convex subset of with nonempty interior that has an isolated maximal element, with respect to the lattice order . Moreover, the ma…
A note on smooth rotund norms which are not midpoint locally uniformly rotund
Carlo Alberto De Bernardi, Alessandro Preti, Jacopo Somaglia
We prove that every separable infinite-dimensional Banach space admits a Gâteaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a similar…
Unit balls of Polyhedral Banach spaces with many extreme points
Carlo Alberto De Bernardi
Let be a -polyhedral Banach space. We show that, for each , admits an -equivalent -polyhedral norm such that the corresponding closed u…
Stochastic Approximation in convex multiobjective optimization
Carlo Alberto De Bernardi, Enrico Miglierina, Elena Molho +1
Given a strictly convex multiobjective optimization problem with objective functions , let us denote by its solution, obtained as minimum point of the linear s…
Rotund Gateaux smooth norms which are not locally uniformly rotund
Carlo Alberto De Bernardi, Jacopo Somaglia
We provide, in every infinite-dimensional separable Banach space, an average locally uniformly rotund (and hence rotund) Gateaux smooth renorming which is not locally uniformly rot…
Extendability of continuous quasiconvex functions from subspaces
Carlo Alberto De Bernardi, Libor Veselý
Let be a subspace of a topological vector space , and an open convex set that intersects . We say that the property [property ] holds if every c…