Zobrazeno 1 - 10
of 70
pro vyhledávání: '"de Bernardi, Carlo"'
We construct a weakly compact convex subset of $\ell^2$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $\ell _+^2$. Moreover, the maximal point cannot be supported by any strictly positive functional, s
Externí odkaz:
http://arxiv.org/abs/2407.10509
We prove that every separable infinite-dimensional Banach space admits a G\^ateaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a similar technique, we provide in every infinite-dimensional Banach space wi
Externí odkaz:
http://arxiv.org/abs/2402.13869
Autor:
De Bernardi, Carlo Alberto
Let $E$ be a $(\mathrm{IV})$-polyhedral Banach space. We show that, for each $\epsilon>0$, $E$ admits an $\epsilon$-equivalent $\mathrm{(V)}$-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its extreme points
Externí odkaz:
http://arxiv.org/abs/2303.10023
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 rotund. This solves an open problem posed by A.J. Guirao, V. Montesinos,
Externí odkaz:
http://arxiv.org/abs/2303.01833
Given a strictly convex multiobjective optimization problem with objective functions $f_1,\dots,f_N$, let us denote by $x_0$ its solution, obtained as minimum point of the linear scalarized problem, where the objective function is the convex combinat
Externí odkaz:
http://arxiv.org/abs/2303.01797
Let $Y$ be a subspace of a topological vector space $X$, and $A\subset X$ an open convex set that intersects $Y$. We say that the property $(QE)$ [property $(CE)$] holds if every continuous quasiconvex [continuous convex] function on $A\cap Y$ admits
Externí odkaz:
http://arxiv.org/abs/2212.13789
Let us consider two sequences of closed convex sets $\{A_n\}$ and $\{B_n\}$ converging with respect to the Attouch-Wets convergence to $A$ and $B$, respectively. Given a starting point $a_0$, we consider the sequences of points obtained by projecting
Externí odkaz:
http://arxiv.org/abs/2007.12486
Autor:
De Bernardi, Carlo Alberto
We provide an elementary proof of a result by V.P.~Fonf and C.~Zanco on point-finite coverings of separable Hilbert spaces. Indeed, by using a variation of the famous argument introduced by J.~Lindenstrauss and R.R.~Phelps \cite{LP} to prove that the
Externí odkaz:
http://arxiv.org/abs/2007.05242
We study star-finite coverings of infinite-dimensional normed spaces. A family of sets is called star-finite if each of its members intersects only finitely many other members of the family. It follows by our results that an LUR or a uniformly Fr\'ec
Externí odkaz:
http://arxiv.org/abs/2002.04308
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 October 2023 526(2)
