Characterization of metric spaces whose free space is isometric to $\ell_1$
Characterization of metric spaces whose free space is isometric to $\ell_1$
We characterize metric spaces whose Lipschitz free space is isometric to $\ell_1$. In particular, we show that 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.