A characterisation of octahedrality in Lipschitz-free spaces

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.

arXiv comment17 pages