Annulé!!! - Plongements des espaces Lipschitz libres dans $ell_1$.
Antonin Prochazka, LMB, Université de Franch-Comté, Besançon
We show that, for a separable and complete metric space M, the Lipschitz-free space F(M) embeds linearly and almost-isometrically into
if and only if M is a subset of an R-tree with length measure 0. Moreover, it embeds isometrically if and only if the length measure of the closure of the set of branching points of M (taken in any minimal R-tree that contains M) is negligible. We also prove that, for any subset M of an R-tree, every extreme point of the unit ball of F(M) is an element of the form (δ(x)−δ(y))/d(x,y) for x≠y∈M. Joint work with R. Aliaga and C. Petitjean.