|
| | | | |
| | | |
| Stat |
Members: 3644
Articles: 2'499'343
Articles rated: 2609
16 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
An infinite Ramsey theorem and some Banach-space dichotomies | | W. T. Gowers
; | | Date: |
7 Dec 2004 | | Journal: | Ann. of Math. (2), Vol. 156 (2002), no. 3, 797--833 | | Subject: | Functional Analysis MSC-class: 46B20 (Primary) 03E02, 03E15, 05D10, 46B03 (Secondary) | math.FA | | Abstract: | 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. | | Source: | arXiv, math.FA/0501105 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER