no. 2
A characterisation of octahedrality in Lipschitz-free spaces
[Une caractérisation de l’octaédralité dans les espaces Lipschitz libres]
Procházka, Antonín1 ; Rueda Zoca, Abraham2
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)
Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 569-588.

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 ℓ 1 et certains espaces de Banach similaires.

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 ℓ 1 and similar Banach spaces.

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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)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Procházka, Antonín; Rueda Zoca, Abraham. A characterisation of octahedrality in Lipschitz-free spaces. Annales de l'Institut Fourier, Tome 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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