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arXiv · 1612.03808

A characterisation of octahedrality in Lipschitz-free spaces

Antonín Procházka·Abraham Rueda Zoca
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Abstract

We characterise the octahedrality of Lipschitz-free space norm in terms of a new geometric property of the underlying metric space. We study the metric spaces with and without this property. Quite surprisingly, metric spaces without this property cannot embed isometrically into $\ell_1$ and similar Banach spaces.

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Antonín Procházka, Abraham Rueda Zoca. 2016-12-12. A characterisation of octahedrality in Lipschitz-free spaces. https://arxiv.org/abs/1612.03808

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