Lipschitz-free spaces over ultrametric spaces

Abstract

We prove that the Lipschitz-free space over a separable ultrametric space has a monotone Schauder basis and is isomorphic to ${\ell }_1$. This extends results of A. Dalet using an alternative approach.

The only change in the latest version is the second author's grant information. Question 1 from the previous version has been answered - see Remark 15 for the solution. Preprint was accepted in Mediterr. J. Math

References in corpus (1)

• Characterization of metric spaces whose free space is isometric to ${\ell }_1$

Cited by in corpus (14)

• On the structure of Lipschitz-free spaces
• The Metric Approximation Property and Lipschitz-Free Spaces over Subsets of ${\mathbb{R}}^N$
• Generalized transportation cost spaces
• Embeddings of Lipschitz-free spaces into ${\ell }_1$
• On relations between transportation cost spaces and ${\ell }_1$
• Lipschitz free $p$-spaces for $0<p<1$
• Isometric embedding of ${\ell }_1$ into Lipschitz-free spaces and ${\ell }_{\infty }$ into their duals
• The Bishop--Phelps--Bollobás property for Lipschitz maps
• Embeddability of ${\ell }_p$ and bases in Lipschitz free $p$-spaces for $0<p\le 1$
• Finitely additive measures and complementability of Lipschitz-free spaces
• Approximation properties in Lipschitz-free spaces over groups
• Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete
• Structure of the Lipschitz free $p$-spaces ${\mathcal{F}}_p({\mathbb{Z}}^d)$ and ${\mathcal{F}}_p({\mathbb{R}}^d)$ for $0<p\le 1$
• Hyperbolic Metric Spaces and Stochastic Embeddings