A lower bound for the equilateral number of normed spaces
| dc.creator | Swanepoel, Konrad J | |
| dc.creator | Villa, Rafael | |
| dc.date | 2006-03-27 | |
| dc.date.accessioned | 2026-07-07T12:51:41Z | |
| dc.date.available | 2026-07-07T12:51:41Z | |
| dc.description | We show that if the Banach-Mazur distance between an n-dimensional normed space X and ell infinity is at most 3/2, then there exist n+1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an arbitrary n-dimensional normed space admits at least e^{c sqrt(log n)} equidistant points, where c>0 is an absolute constant. We also show that there exist n equidistant points in spaces sufficiently close to n-dimensional ell p (1 < p < infinity). | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603614 | |
| dc.identifier | http://arxiv.org/abs/math/0603614 | |
| dc.identifier | Proc. Amer. Math. Soc. 136 (2008), 127--131. | |
| dc.identifier | doi:10.1090/S0002-9939-07-08916-2 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223073 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B04 (Primary); 46B20, 52A21, 52C17 (Secondary) | |
| dc.title | A lower bound for the equilateral number of normed spaces | |
| dc.type | text |