A lower bound for the equilateral number of normed spaces

被引：13
|
作者：
Swanepoel, Konrad J.
Villa-Caro, Rafael
机构：
[1] Univ S Africa, Dept Math Sci, ZA-0003 Pretoria, South Africa
[2] Univ Seville, Fac Math, Dept Math Anal, E-41012 Seville, Spain
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 01期
关键词：
D O I：
10.1090/S0002-9939-07-08916-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that if the Banach-Mazur distance between an n-dimensional normed space X and l(infinity)(n) 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 root 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 l(p)(n), 1 < p < infinity.
引用
收藏
页码：127 / 131
页数：5
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