5 papers · 1 filter
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…
Asymptotic and nonlinear geometries of Banach spaces and their interactions
Florent P. Baudier, Gilles Lancien
This book discusses the interactions between the (nonlinear) metric structure of Banach spaces and their linear asymptotic behavior. The overarching problem is to understand how th…
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…
An asymptotic analog of a local-to-global phenomenon for uniformly convex renormings
Florent P. Baudier, Gilles Lancien
In this note, we investigate the renorming theory of Banach spaces with property of Rolewicz. In particular, we give a "coordinate-free" proof of the fact that every Banach s…