A lower bound for the equilateral number of normed spaces

dc.creatorSwanepoel, Konrad J
dc.creatorVilla, Rafael
dc.date2006-03-27
dc.date.accessioned2026-07-07T12:51:41Z
dc.date.available2026-07-07T12:51:41Z
dc.descriptionWe 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.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0603614
dc.identifierhttp://arxiv.org/abs/math/0603614
dc.identifierProc. Amer. Math. Soc. 136 (2008), 127--131.
dc.identifierdoi:10.1090/S0002-9939-07-08916-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223073
dc.subjectMetric Geometry
dc.subjectFunctional Analysis
dc.subject46B04 (Primary); 46B20, 52A21, 52C17 (Secondary)
dc.titleA lower bound for the equilateral number of normed spaces
dc.typetext

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