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

Abstract

We characterize metric spaces whose Lipschitz free space is isometric to ${\ell }_1$. In particular, the Lipschitz free space over an ultrametric space is not isometric to ${\ell }_1(\Gamma )$ for any set $\Gamma$. We give a lower bound for the Banach-Mazur distance in the finite case.

Cited by in corpus (1)

• Lipschitz-free spaces over ultrametric spaces