A characterisation of octahedrality in Lipschitz-free spaces

Published 12 Dec 2016 in math.FA | (1612.03808v1)

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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