12 citations · 66 across the 20 of their papers we have counts for
22 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…
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…
Norming Markushevich bases: recent results and open problems
Petr Hájek, Tommaso Russo
We survey several results concerning norming Markushevich bases (M-bases, for short), focusing in particular on two recent examples of a weakly compactly generated Banach space wit…
Tilings of the Hyperbolic Space and Lipschitz Functions
Christian Bargetz, Franz Luggin, Tommaso Russo
We use a special tiling for the hyperbolic -space for to construct an (almost) explicit isomorphism between the Lipschitz-free space $\mathcal{F}(\mathb…
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…
Smooth norms in dense subspaces of and operator ranges
Sheldon Dantas, Petr Hájek, Tommaso Russo
For , we prove that the dense subspace of comprising all elements such that for some admits a $C^{\i…
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…
Smooth and polyhedral norms via fundamental biorthogonal systems
Sheldon Dantas, Petr Hájek, Tommaso Russo
Let be a Banach space with a fundamental biorthogonal system and let be the dense subspace spanned by the vectors of the system. We prove that $\mathcal…
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…
Projecting Lipschitz functions onto spaces of polynomials
Petr Hájek, Tommaso Russo
The Banach space of -homogeneous polynomials on the Banach space can be naturally embedded in the Banach space of real-valued Lipsc…
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…
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…
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…
Smooth norms in dense subspaces of Banach spaces
Sheldon Dantas, Petr Hájek, Tommaso Russo
In the first part of our paper, we show that has a dense linear subspace which admits an equivalent real analytic norm. As a corollary, every separable Banach space,…
On densely isomorphic normed spaces
Petr Hájek, Tommaso Russo
In the first part of our note we prove that every Weakly Lindelöf Determined (WLD) (in particular, every reflexive) non-separable Banach space contains two dense linear subspac…
A note on symmetric separation in Banach spaces
Tommaso Russo
We present some new results on the symmetric Kottman's constant of a Banach space and its relationship with the Kottman constant. We show that , for every in…
An uncountable version of Pták's combinatorial lemma
Petr Hájek, Tommaso Russo
In this note we are concerned with the validity of an uncountable analogue of a combinatorial lemma due to Vlastimil Pták. We show that the validity of the result for can not…
Separated sets and Auerbach systems in Banach spaces
Petr Hájek, Tomasz Kania, Tommaso Russo
The paper elucidates the relationship between the density of a Banach space and possible sizes of well-separated subsets of its unit sphere. For example, it is proved that for a la…
Symmetrically separated sequences in the unit sphere of a Banach space
Petr Hájek, Tomasz Kania, Tommaso Russo
We prove the symmetric version of Kottman's theorem, that is to say, we demonstrate that the unit sphere of an infinite-dimensional Banach space contains an infinite subset wit…
Some remarks on smooth renormings of Banach spaces
Petr Hájek, Tommaso Russo
We prove that in every separable Banach space with a Schauder basis and a -smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with…