A characterisation of octahedrality in Lipschitz-free spaces
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, p. 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.
Received : 2017-01-20
Revised : 2017-05-05
Accepted : 2017-06-15
Published online : 2018-04-18
DOI : https://doi.org/10.5802/aif.3171
Classification:  46B04,  46B20,  46B85
Keywords: Octahedrality, Free spaces, Uniformly discrete metric spaces
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {2},
     year = {2018},
     pages = {569-588},
     doi = {10.5802/aif.3171},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2018__68_2_569_0}
}
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/item/AIF_2018__68_2_569_0/

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