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Article Dans Une Revue Journal of Functional Analysis Année : 2021

Embeddings of Lipschitz-free spaces into ℓ1

Résumé

We show that, for a separable and complete metric space M , the Lipschitz-free space F(M) embeds linearly and almost-isometrically into 1 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 .
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Dates et versions

hal-02974707 , version 1 (22-10-2020)

Identifiants

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Ramón J. Aliaga, Colin Petitjean, Antonin Prochazka. Embeddings of Lipschitz-free spaces into ℓ1. Journal of Functional Analysis, 2021, 280 (6), pp.108916. ⟨10.1016/j.jfa.2020.108916⟩. ⟨hal-02974707⟩
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