47 citations · 225 across the 22 of their papers we have counts for
22 papers
On the weak separability of the space of Lipschitz functions
Leandro Candido, Marek Cuth, Benjamin Vejnar
We conjecture that whenever is a metric space of density at most continuum, then the space of Lipschitz functions is -separable. We prove the conjecture for several classe…
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…
Lipschitz algebras and Lipschitz-free spaces over unbounded metric spaces
Fernando Albiac, Jose L. Ansorena, Marek Cuth +1
We present a way to turn an arbitrary (unbounded) metric space into a bounded metric space in such a way that the corresponding Lipschitz-free spaces $\…
Lipschitz free spaces isomorphic to their infinite sums and geometric applications
Fernando Albiac, Jose L. Ansorena, Marek Cuth +1
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct -sum and exhibit several applications. As examples o…
Structure of the Lipschitz free -spaces and for
Fernando Albiac, Jose L. Ansorena, Marek Cuth +1
Our aim in this article is to contribute to the theory of Lipschitz free -spaces for over the Euclidean spaces and . To that end, on one…
Polish spaces of Banach spaces
Marek Cúth, Martin Doležal, Michal Doucha +1
We present and thoroughly study natural Polish spaces of separable Banach spaces. These spaces are defined as spaces of norms, resp. pseudonorms, on the countable infinite-dimensio…
Embeddability of and bases in Lipschitz free -spaces for
Fernando Albiac, Jose L. Ansorena, Marek Cuth +1
Our goal in this paper is to continue the study initiated by the authors in [Lipschitz free -spaces for ; arXiv:1811.01265 [math.FA]] of the geometry of the Lipschitz fre…
Lipschitz free -spaces for
Fernando Albiac, Jose L. Ansorena, Marek Cuth +1
This paper initiates the study of the structure of a new class of -Banach spaces, , namely the Lipschitz free -spaces (alternatively called Arens-Eells -spaces) $\m…
Finitely additive measures and complementability of Lipschitz-free spaces
Marek Cúth, Ondřej F. K. Kalenda, Petr Kaplický
We prove in particular that the Lipschitz-free space over a finitely-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective project…
Separable determination in Banach spaces
Marek Cuth
We study a relation between three different formulations of theorems on separable determination - one using the concept of rich families, second via the concept of suitable models…
Rich families and projectional skeletons in Asplund WCG spaces
Marek Cuth, Marian Fabian
We show a way of constructing projectional skeletons using the concept of rich families in Banach spaces which admit a projectional generator. Our next result is that a Banach spac…
Separable determination of (generalized-)lushness
Marek Cuth
We prove that every Asplund lush space is generalized-lush using the method of separable reduction. This gives a partial positive answer to a question by Jan-David Hardtke.
Separable reduction of Frechet subdifferentiability in Asplund spaces
Marek Cuth, Marian Fabian
In the framework of Asplund spaces, we use two equivalent instruments - rich families and suitable models from logic - for performing separable reductions of various statements on…
On the structure of Lipschitz-free spaces
Marek Cuth, Michal Doucha, Przemyslaw Wojtaszczyk
In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of $\…
Lipschitz-free spaces over ultrametric spaces
Marek Cuth, Michal Doucha
We prove that the Lipschitz-free space over a separable ultrametric space has a monotone Schauder basis and is isomorphic to . This extends results of A. Dalet using an alt…
Characterization of compact monotonically ()-monolithic spaces using system of retractions
Marek Cuth
We prove that a compact space is monotonically Sokolov if and only if it is monotonically -monolithic. This gives answers to several questions of R. Rojas-Hernandez and V. V. Tk…
On Separable Determination of Sigma-P-Porous Sets in Banach Spaces
Marek Cuth, Martin Rmoutil, Miroslav Zeleny
We use a method involving elementary submodels and a partial converse of Foran lemma to prove separable reduction theorems concerning Suslin sigma-P-porous sets where "P" can be fr…
Rich families and elementary submodels
Marek Cuth, Ondrej F. K. Kalenda
We compare two methods of proving separable reduction theorems in functional analysis -- the method of rich families and the method of elementary submodels. We show that any result…
Simultaneous projectional skeletons
Marek Cuth
We prove the existence of a simultaneous projectional skeleton for certain subspaces of spaces. This generalizes a result on simultaneous projectional resolutions…
Projections in duals to Asplund spaces made without Simons' lemma
Marek Cuth, Marian Fabian
G. Godefroy and the second author of this note proved in 1988 that in duals to Asplund spaces there always exists a projectional resolution of the identity. A few years later, Ch.…
Noncommutative Valdivia compacta
Marek Cuth
We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleto…
Sigma-porosity is separably determined
Marek Cúth, Martin Rmoutil
We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlar…