14 citations · 46 across the 21 of their papers we have counts for
27 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…
Tilings and coverings by balls in
Carlo Alberto De Bernardi, Tommaso Russo, Şeyda Sezgek +1
A famous result of Klee from 1981 is that the Banach space admits a disjoint tiling by balls of radius , for all cardinals with . Klee also observed that…
Packings in classical Banach spaces
Carlo Alberto De Bernardi, Tommaso Russo, Şeyda Sezgek +1
We obtain several new results on the simultaneous packing and covering constant of a Banach space , and its lattice counterpart . Th…
Global Lipschitz extension preserving the slope
Nicolò De Ponti, Jacopo Somaglia
We show that every real-valued Lipschitz function on a subset of a metric space can be extended to the whole space while preserving the slope and, up to a small error, the global L…
Nonexistence results for the semilinear wave equation on graphs
Dario Daniele Monticelli, Fabio Punzo, Jacopo Somaglia
We investigate the semilinear wave equation with potential on weighted graphs. We establish sufficient conditions for the nonexistence of global-in-time solutions. Both nonnegative…
Lattice tilings of Hilbert spaces
Carlo Alberto De Bernardi, Tommaso Russo, Jacopo Somaglia
We construct a bounded and symmetric convex body in (for certain cardinals ) whose translates yield a tiling of . This answers a question due to Fonf and…
Some remarks on almost locally uniformly rotund points
Carlo Alberto De Bernardi, Jacopo Somaglia
We study the relations between different notions of almost locally uniformly rotund points that appear in literature. We show that every non-reflexive Banach space admits an equiva…
Moduli of continuity and absolute continuity: any relation?
Matteo Muratori, Jacopo Somaglia
We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is…
Nonexistence of solutions to parabolic problems with a potential on weighted graphs
Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia
We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper…
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…
Nonexistence results for semilinear elliptic equations on weighted graphs
Dario Daniele Monticelli, Fabio Punzo, Jacopo Somaglia
We study semilinear elliptic inequalities with a potential on infinite graphs. Given a distance on the graph, we assume an upper bound on its Laplacian, and a growth condition on a…
Banach spaces of continuous functions without norming Markushevich bases
Tommaso Russo, Jacopo Somaglia
We investigate the question whether a scattered compact topological space such that has a norming Markushevich basis (M-basis, for short) must be Eberlein. This question…
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…
Dense lineability and spaceability in certain subsets of
Paolo Leonetti, Tommaso Russo, Jacopo Somaglia
We investigate dense lineability and spaceability of subsets of with a prescribed number of accumulation points. We prove that the set of all bounded sequences with e…
Characterizations of weakly -analytic and Vašák spaces using projectional skeletons and separable PRI
Claudia Correa, Marek Cúth, Jacopo Somaglia
We find characterizations of Vašák spaces and weakly -analytic spaces using the notions of separable projectional resolution of the identity (SPRI) and of projectional…
Weakly Corson compact trees
Tommaso Russo, Jacopo Somaglia
We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns ever…
Small semi-Eberlein compacta and inverse limits
Claudia Correa, Tommaso Russo, Jacopo Somaglia
We study properties of semi-Eberlein compacta related to inverse limits. We concentrate our investigation on an interesting subclass of small semi-Eberlein compacta whose elements…
Characterization of (semi-)Eberlein compacta using retractional skeletons
Claudia Correa, Marek Cúth, Jacopo Somaglia
We deeply study retractions associated to suitable models in compact spaces admitting a retractional skeleton and find several interesting consequences. Most importantly, we provid…
An Asplund space with norming Markuševič basis that is not weakly compactly generated
Petr Hájek, Tommaso Russo, Jacopo Somaglia +1
We construct an Asplund Banach space with a norming Markuševič basis such that is not weakly compactly generated. This solves a long-standing open probl…
Star-finite coverings of Banach spaces
Carlo Alberto De Bernardi, Jacopo Somaglia, Libor Vesely
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 t…
Overcomplete sets in non-separable Banach spaces
Tommaso Russo, Jacopo Somaglia
We introduce and study the notion of overcomplete set in a Banach space, that subsumes and extends the classical concept of overcomplete sequence in a (separable) Banach space. We…
On bisequentiality and spaces of strictly decreasing functions on trees
Claudio Agostini, Jacopo Somaglia
We present a characterization of spaces of strictly decreasing functions on trees in terms of bisequentiality. This characterization answers Questions 6.1 and 6.2 of "A filter on a…
On compact trees with the coarse wedge topology
Jacopo Somaglia
In the present paper we investigate the class of compact trees, endowed with the coarse wedge topology, in the area of non-separable Banach spaces. We describe Valdivia compact tre…