Artículo
A lower bound for the equilateral number of normed spaces
Autor/es | Swanepoel, Konrad J.
Villa Caro, Rafael |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2008 |
Fecha de depósito | 2016-06-03 |
Publicado en |
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Resumen | We show that if the Banach-Mazur distance between an n-dimensional normed space X and ℓ 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 ... We show that if the Banach-Mazur distance between an n-dimensional normed space X and ℓ 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 √ 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 n p , 1 < p < ∞. |
Agencias financiadoras | South African National Research Foundation Dirección General de Enseñanza Superior. España |
Identificador del proyecto | 2053752
BFM2003-01297 |
Cita | Swanepoel, K.J. y Villa Caro, R. (2008). A lower bound for the equilateral number of normed spaces. Proceedings of the American Mathematical Society, 136 (1), 127-131. |
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