14 citations · 46 across the 21 of their papers we have counts for
15 papers · 1 filter
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…
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…
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…
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…
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…
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 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…
Almost overcomplete and almost overtotal sequences in Banach spaces
Vladimir P. Fonf, Clemente Zanco
The new concepts are introduced of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such sequences is relatively n…