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.
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.
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Keywords: Octahedrality, Free spaces, Uniformly discrete metric spaces
Mot 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{\textquoteright}institut Fourier}, volume = {68}, number = {2}, year = {2018}, doi = {10.5802/aif.3171}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.3171/} }
TY - JOUR AU - Procházka, Antonín AU - Rueda Zoca, Abraham TI - A characterisation of octahedrality in Lipschitz-free spaces JO - Annales de l'Institut Fourier PY - 2018 SP - 569 EP - 588 VL - 68 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3171/ DO - 10.5802/aif.3171 LA - en ID - AIF_2018__68_2_569_0 ER -
%0 Journal Article %A Procházka, Antonín %A Rueda Zoca, Abraham %T A characterisation of octahedrality in Lipschitz-free spaces %J Annales de l'Institut Fourier %D 2018 %P 569-588 %V 68 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3171/ %R 10.5802/aif.3171 %G en %F AIF_2018__68_2_569_0
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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