14 papers · 1 filter
Lipschitz extension and Lipschitz-free spaces over nets in normed spaces
Ramón J. Aliaga, Rubén Medina
We consider subsets of a metric space such that Lipschitz mappings defined on can be extended to Lipschitz mappings on , and we show that the union of such subsets h…
Transportation cost spaces and stochastic trees
Rubén Medina, Garrett Tresch
We study transportation cost spaces over finite metric spaces, also known as Lipschitz free spaces. Our work is motivated by a core problem posed by S. Dilworth, D. Kutzarova and M…
Non-uniformly continuous nearest point maps
Rubén Medina, Andrés Quilis
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not unif…
The equivalence between CPCP and strong regularity under Krein-Milman property
Ginés López-Pérez, Rubén Medina
We obtain a result in the spirit of the well-known W. Schachermeyer and H. P. Rosenthal research about the equivalence between Radon-Nikodym and Krein-Milman properties, by showing…
A characterisation of the Daugavet property in spaces of vector-valued Lipschitz functions
Rubén Medina, Abraham Rueda Zoca
Let be a metric space and be a Banach space. In this paper we address several questions about the structure of and .…
On the constant of Lipschitz approximability
Rubén Medina
In this note we find and give an explicit construction of a separable Banach space such that there is no -Lipschitz retraction from onto any compact convex subset…
On isometric embeddings into the set of strongly norm-attaining Lipschitz functions
Sheldon Dantas, Rubén Medina, Andrés Quilis +1
In this paper, we provide an infinite metric space such that the set $\mbox{SNA}(M)$ of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometr…
On holomorphic functions attaining their weighted norms
Sheldon Dantas, Rubén Medina
We study holomorphic functions attaining weighted norms and its connections with the classical theory of norm attaining holomorphic functions. We prove that there are polynomials o…
Compact Hölder retractions and nearest point maps
Rubén Medina
In this paper, two main results concerning uniformly continuous retractions are proved. First, an -Hölder retraction from any separable Banach space onto a compact convex subset…
Retractions and the bounded approximation property in Banach spaces
Petr Hájek, Rubén Medina
In the present paper we prove that a necessary condition for a Banach space to admit a generating compact Lipschitz retract , which satisfies an additional mild assumption o…
Schauder basis in Lipschitz free spaces over nets of -spaces
Petr Hájek, Rubén Medina
In the present note we give a construction (based on a retractional argument) of a Schauder basis for the Lipschitz free space , over a net in any separable inf…
Schauder bases in Lipschitz free spaces over nets in Banach spaces
Petr Hájek, Rubén Medina
In the present note we give two explicit constructions (based on a retractional argument) of a Schauder basis for the Lipschitz free space , over certain uniformly…
Compact retractions and Schauder decompositions in Banach spaces
Petr Hájek, Rubén Medina
In our note we show the very close connection between the existence of a Finite Dimensional Decomposition (FDD for short) for a separable Banach space and the existence of a Li…
A characterization of the weak topology in the unit ball of purely atomic preduals
Ginés López-Pérez, Rubén Medina
We study Banach spaces with a weak stable unit ball, that is Banach spaces where every convex combination of relatively weakly open subsets in its unit ball is again a relatively w…