On Asymptotically Symmetric Banach Spaces
| dc.creator | Junge, M. | |
| dc.creator | Kutzarova, D. | |
| dc.creator | Odell, E. | |
| dc.date | 2005-08-01 | |
| dc.date.accessioned | 2026-07-07T05:22:09Z | |
| dc.date.available | 2026-07-07T05:22:09Z | |
| dc.description | We define and study asymptotically symmetric Banach spaces (a.s.) and its variations: weakly a.s. (w.a.s.) and weakly normalized a.s. (w.n.a.s.). If X is a.s. then all spreading models of X are uniformly symmetric. We show that the converse fails. We also show that w.a.s. and w.n.a.s. are not equivalent properties and that Schlumprecht's space S fails to be w.n.a.s. We show that if X is separable and has the property that every normalized weakly null sequence in X has a subsequence equivalent to the unit vector basis of c_0 then X is w.a.s.. We obtain an analogous result if c_0 is replaced by ell_1 and also show it is false if c_0 is replaced by ell_p, 1 < p < infinity. We prove that if 1 less than or equal p < infinity and the norm of the sum of (x_i)_1^n is of the order n^{1/p} for all (x_i)_1^n in the n^{th} asymptotic structure of $X$, then X contains an asymptotic ell_p, hence w.a.s. subspace. | |
| dc.description | 22 pages, AMSLaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0508035 | |
| dc.identifier | http://arxiv.org/abs/math/0508035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75950 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B03; 46B20 | |
| dc.title | On Asymptotically Symmetric Banach Spaces | |
| dc.type | text |