An infinite Ramsey theorem and some Banach-space dichotomies
| dc.creator | Gowers, W. T. | |
| dc.date | 2005-01-07 | |
| dc.date.accessioned | 2026-07-07T05:15:54Z | |
| dc.date.available | 2026-07-07T05:15:54Z | |
| dc.description | A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic nature which implies an interesting dichotomy for subspaces of Banach spaces. Combined with a result of Komorowski and Tomczak-Jaegermann, this gives a positive answer to Banach's problem. We then generalize the Ramsey-theoretic result and deduce a further dichotomy for Banach spaces with an unconditional basis. | |
| dc.description | 37 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0501105 | |
| dc.identifier | http://arxiv.org/abs/math/0501105 | |
| dc.identifier | Ann. of Math. (2), Vol. 156 (2002), no. 3, 797--833 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73792 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20 (Primary) 03E02, 03E15, 05D10, 46B03 (Secondary) | |
| dc.title | An infinite Ramsey theorem and some Banach-space dichotomies | |
| dc.type | text |