7 citations · 15 across the 16 of their papers we have counts for
17 papers · 1 filter
The Ball-Covering Property in Lipschitz-Free Spaces
Ramón J. Aliaga, Colin Petitjean, Antonín Procházka +1
We study ball-covering properties in Lipschitz-free spaces. We establish an extension criterion for proving that fails the ball-covering property and apply it to se…
Lipschitz-free spaces are strongly unique preduals
Ramón J. Aliaga, Marek Cúth, Felipe Vico
We prove that the Lipschitz-free space is the strongly unique isometric predual of for every metric space , solving a longstanding open prob…
The unique predual problem for Lipschitz spaces, revisited
Ramón J. Aliaga, Felipe Vico
In his 2018 paper ``On the unique predual problem for Lipschitz spaces'', N. Weaver published proofs that Banach spaces of Lipschitz functions on a complete met…
Lipschitz-free spaces over non-porous subsets of
Ramón J. Aliaga
We prove that the Lipschitz-free space contains a complemented copy of whenever is not porous. Consequently, if…
Lipschitz-free spaces and purely 1-unrectifiable metric spaces
Ramón J. Aliaga
The Lipschitz-free space is a canonical linearization of a complete metric space whose topological dual is the space of Lipschitz functions on . We review t…
Integral representations of projective norm-attaining tensors
Ramón J. Aliaga, Sheldon Dantas, Juan Guerrero-Viu +2
We introduce a Bochner integral approach to projective norm attainment in tensor products of Banach spaces by defining the class of integral projective norm-attaining tensors. This…
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…
On Weak Compactness and Uniform Regularity in Lipschitz free Spaces
Ramón J. Aliaga, Colin Petitjean, Antonín Prochazka +1
We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space , weakly precompact sets in the Lipsc…
Almost preserved extreme points
Ramón J. Aliaga, Luis C. García-Lirola, Juan Guerrero-Viu +2
In this paper we introduce the notion of an almost preserved extreme point (APEP) of a set as a weakening of the concept of preserved extreme points, and we systematically study su…
Lipschitz spaces over non-porous sets
Ramón J. Aliaga
Let be a subset of . If is not porous, in particular if it has positive -dimensional Lebesgue measure, we prove that the Lipschitz spaces $\mathrm{Lip}_0(M…
A solution to the extreme point problem and other applications of Choquet theory to Lipschitz-free spaces
Ramón J. Aliaga, Eva Pernecká, Richard J. Smith
We prove that every element of a Lipschitz-free space admits an expression as a convex series of elements with compact support. As a consequence, we conclude that all extreme point…
Pełczyński's property (V) in Lipschitz-free spaces
Ramón J. Aliaga, Eva Pernecká, Alicia Quero
We prove that Pelczyński's property (V) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal{F}(M)…
De Leeuw representations of functionals on Lipschitz spaces
Ramón J. Aliaga, E. Pernecká, Richard J. Smith
Let be the space of Lipschitz functions on a complete metric space that vanish at a point . We investigate its dual using…
A note on nonseparable Lipschitz-free spaces
Ramón J. Aliaga, Guillaume Grelier, Antonín Procházka
We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property (), Talponen…
A relative version of Daugavet-points and the Daugavet property
Trond A. Abrahamsen, Ramón J. Aliaga, Vegard Lima +4
We introduce relative versions of Daugavet-points and the Daugavet property, where the Daugavet-behavior is localized inside of some supporting slice. These points present striking…
Delta-points and their implications for the geometry of Banach spaces
Trond A. Abrahamsen, Ramón J. Aliaga, Vegard Lima +4
We show that the Lipschitz-free space with the Radon--Nikodým property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to . Furthermo…
Convex integrals of molecules in Lipschitz-free spaces
Ramón J. Aliaga, Eva Pernecká, Richard J. Smith
We introduce convex integrals of molecules in Lipschitz-free spaces as a continuous counterpart of convex series considered elsewhere, based on the de Leeuw repres…