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arXiv · 1502.02719

Characterization of metric spaces whose free space is isometric to $\ell_1$

Aude Dalet·Pedro L. Kaufmann·Antonín Procházka
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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.

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Aude Dalet, Pedro L. Kaufmann, Antonín Procházka. 2015-02-09. Characterization of metric spaces whose free space is isometric to $\ell_1$. https://arxiv.org/abs/1502.02719

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