A NEW COARSELY RIGID CLASS OF BANACH SPACES
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | A NEW COARSELY RIGID CLASS OF BANACH SPACES |
| Type de publication | Journal Article |
| Year of Publication | 2021 |
| Auteurs | Baudier F., Lancien G., Motakis P., Schlumprecht T. |
| Journal | JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU |
| Volume | 20 |
| Pagination | PII S1474748019000732 |
| Date Published | SEP |
| Type of Article | Article |
| ISSN | 1474-7480 |
| Mots-clés | asymptotic-c(0) spaces, Coarse embeddings, coarsely rigid classes of banach spaces, Hamming graphs |
| Résumé | We prove that the class of reflexive asymptotic-c(0) Banach spaces is coarsely rigid, meaning that if a Banach space X coarsely embeds into a reflexive asymptotic-c(0) space Y, then X is also reflexive and asymptotic-c(0). In order to achieve this result, we provide a purely metric characterization of this class of Banach spaces. This metric characterization takes the form of a concentration inequality for Lipschitz maps on the Hamming graphs, which is rigid under coarse embeddings. Using an example of a quasi-reflexive asymptotic-c(0) space, we show that this concentration inequality is not equivalent to the non-equi-coarse embeddability of the Hamming graphs. |
| DOI | 10.1017/S1474748019000732 |