5 papers
On metric characterizations of tree and fragmentability indices of Banach spaces
Estelle Basset, Gilles Lancien, Antonin Procházka
We introduce two ordinal indices that are linear invariants for Banach spaces: the dyadic tree index and the sprawling tree index. We show that they are also bi-Lipschitz invariant…
Composition operators for holomorphic Lipschitz functions
Verónica Dimant, Luis C. García-Lirola, Juan Guerrero-Viu +1
We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of t…
Diversity of Lipschitz-free spaces over countable complete discrete metric spaces
Estelle Basset, Gilles Lancien, Antonín Procházka
We show that there are uncountably many mutually non-isomorphic Lipschitz-free spaces over countable, complete, discrete metric spaces. Also there is a countable, complete, discret…
On curve-flat Lipschitz functions and their linearizations
Gonzalo Flores, Mingu Jung, Gilles Lancien +3
We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization of a…
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…