The geometry of Hamming-type metrics and their embeddings into Banach spaces - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Israel Journal of Mathematics Année : 2021

The geometry of Hamming-type metrics and their embeddings into Banach spaces

Florent Baudier
  • Fonction : Auteur
Pavlos Motakis
  • Fonction : Auteur
Thomas H Schlumprecht
  • Fonction : Auteur

Résumé

Within the class of reflexive Banach spaces, we prove a metric characterization of the class of asymptotic-c 0 spaces in terms of a bi-Lipschitz invariant which involves metrics that generalize the Hamming metric on k-subsets of N. We apply this characterization to show that the class of separable, reflexive, and asymptotic-c 0 Banach spaces is non-Borel co-analytic. Finally, we introduce a relaxation of the asymptotic-c 0 property, called the asymptotic-subsequential-c 0 property, which is a partial obstruction to the equi-coarse embeddability of the sequence of Hamming graphs. We present examples of spaces that are asymptotic-subsequential-c 0. In particular T * (T *) is asymptotic-subsequential-c 0 where T * is Tsirelson's original space.
Fichier principal
Vignette du fichier
blms3_arxiv.pdf (335.7 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03377420 , version 1 (14-10-2021)

Identifiants

Citer

Florent Baudier, Gilles Lancien, Pavlos Motakis, Thomas H Schlumprecht. The geometry of Hamming-type metrics and their embeddings into Banach spaces. Israel Journal of Mathematics, 2021, ⟨10.1007/s11856-021-2187-0⟩. ⟨hal-03377420⟩
29 Consultations
92 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More