6 papers · 1 filter
Compact and weakly compact Lipschitz operators
Arafat Abbar, Clément Coine, Colin Petitjean
Any Lipschitz map between two pointed metric spaces may be extended in a unique way to a bounded linear operator betwe…
On the dynamics of Lipschitz operators
Arafat Abbar, Clément Coine, Colin Petitjean
By the linearization property of Lipschitz-free spaces, any Lipschitz map between two pointed metric spaces may be extended uniquely to a bounded linear operator $\wi…
On Kalton's interlaced graphs and nonlinear embeddings into dual Banach spaces
Bruno de Mendonça Braga, Gilles Lancien, Colin Petitjean +1
We study the nonlinear embeddability of Banach spaces and the equi-embeddability of the family of Kalton's interlaced graphs into dual spaces. Not…
On exposed points of Lipschitz free spaces
Colin Petitjean, Antonín Procházka
In this note we prove that a molecule is an exposed point of the unit ball of a Lispchitz free space if and only if the metric segment $[x,…
On the coarse geometry of James spaces
Gilles Lancien, Colin Petitjean, Antonín Procházka
In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space nor into its dual . It is a particular case of a…
Extremal structure and Duality of Lipschitz free spaces
Luis García-Lirola, Colin Petitjean, Antonin Procházka +1
We analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points). We prove in particular th…