11 papers
Lipschitz-free spaces over non-porous subsets of
Ramón J. Aliaga, Ramón J. Aliaga
We prove that the Lipschitz-free space contains a complemented copy of whenever is not porous. Consequently, if…
Almost preserved extreme points
Ramón J. Aliaga, Luis C. GarcÃa-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 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…
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…
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…
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…