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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DOI: 10.5802/aif.3171
Classification: 46B04, 46B20, 46B85
Keywords: Octahedrality, Free spaces, Uniformly discrete metric spaces
Mot clés : Octaédralité, Espaces Lipschitz libres, Espaces métriques uniformément discrets
Procházka, Antonín 1; Rueda Zoca, Abraham 2

1 Université Bourgogne Franche-Comté Laboratoire de Mathématiques UMR 6623 16 route de Gray 25030 Besançon Cedex (France)
2 Universidad de Granada, Facultad de Ciencias Departamento de Análisis Matemático 18071-Granada (Spain)
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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. http://www.numdam.org/articles/10.5802/aif.3171/

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