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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, the Lipschitz free space over an ultrametric space is not isometric to $\ell_1(Γ)$ for any set $Γ$. We give a lower bound for the Banach-Mazur distance in the finite case.

preprint2015arXivOpen access
Aude DaletPedro L. KaufmannAntonín Procházka
math.FA
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Open access3 authors1 topic
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Aude DaletPedro L. KaufmannAntonín Procházka

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