A characterisation of octahedrality in Lipschitz-free spaces
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 569-588.

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 be embedded isometrically into 1 and similar Banach spaces.

On caractérise l’octaédralité de la norme d’un espace Lipschitz libre par le biais d’une nouvelle propriété géométrique de l’espace métrique sous-jacent. Nous étudions les espaces métriques avec et sans cette propriété. Par exemple, les espaces sans cette propriété ne se plongent pas isométriquement dans 1 et certains espaces de Banach similaires.

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Published online:
DOI: 10.5802/aif.3171
Classification: 46B04,  46B20,  46B85
Keywords: Octahedrality, Free spaces, Uniformly discrete metric spaces
License: CC-BY-ND 4.0
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Procházka, Antonín; Rueda Zoca, Abraham. A characterisation of octahedrality in Lipschitz-free spaces. Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 569-588. doi : 10.5802/aif.3171. https://aif.centre-mersenne.org/articles/10.5802/aif.3171/

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