Lipschitz-free spaces over ultrametric spaces

TL;DR

This paper proves that Lipschitz-free spaces over separable ultrametric spaces have a monotone Schauder basis and are isomorphic to , extending previous results with a new approach.

Contribution

It introduces an alternative proof that Lipschitz-free spaces over separable ultrametric spaces are isomorphic to  and possess a monotone Schauder basis.

Findings

Lipschitz-free spaces over separable ultrametric spaces are isomorphic to .

Such spaces have a monotone Schauder basis.

The result extends previous work by A. Dalet.

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.