ASYMPTOTIC AND COARSE LIPSCHITZ STRUCTURES OF QUASI-REFLEXIVE BANACH SPACES
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | ASYMPTOTIC AND COARSE LIPSCHITZ STRUCTURES OF QUASI-REFLEXIVE BANACH SPACES |
| Type de publication | Journal Article |
| Year of Publication | 2018 |
| Auteurs | Lancien G., Raja M. |
| Journal | HOUSTON JOURNAL OF MATHEMATICS |
| Volume | 44 |
| Pagination | 927-940 |
| Type of Article | Article |
| ISSN | 0362-1588 |
| Mots-clés | asymptotic structure of Banach spaces, coarse Lipschitz embeddings, quasi-reflexive Banach spaces |
| Résumé | In this note, we extend to the setting of quasi-reflexive spaces a classical result of N. Kalton and L. Randrianarivony on the coarse Lipschitz structure of reflexive and asymptotically uniformly smooth Banach spaces. As an application, we show for instance, that for 1 <= q < p, a q-asymptotically uniformly convex Banach space does not coarse Lipschitz embed into a p-asymptotically uniformly smooth quasi-reflexive Banach space. This extends a recent result of B.M. Braga. |