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 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 and similar Banach spaces.
Révisé le : 2017-05-04
Accepté le : 2017-06-14
Publié le : 2018-04-17
Classification : 46B04, 46B20, 46B85
Mots clés : Octaédralité, Espaces Lipschitz libres, Espaces métriques uniformément discrets
@article{AIF_2018__68_2_569_0,
author = {Proch\'azka, Anton\'\i n and Rueda Zoca, Abraham},
title = {A characterisation of octahedrality in Lipschitz-free spaces},
journal = {Annales de l'Institut Fourier},
pages = {569--588},
publisher = {Association des Annales de l'institut Fourier},
volume = {68},
number = {2},
year = {2018},
doi = {10.5802/aif.3171},
language = {en},
url = {archive.numdam.org/item/AIF_2018__68_2_569_0/}
}
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. http://archive.numdam.org/item/AIF_2018__68_2_569_0/
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