On Nearly Equilateral Simplices and Nearly l8 Spaces

Autores: Gennadiy Averkov
Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 394-397
Idioma: inglés
DOI: 10.4153/cmb-2010-055-1
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Resumen
- By d(X,Y) we denote the (multiplicative) Banach-Mazur distance between two normed spaces X and Y. Let X be an n-dimensional normed space with d(X,l8n) = 2, where l8n stands for Rn endowed with the norm ||(x1,...,xn)||8 : = max{|x1|,..., |xn| }. Then every metric space (S,?) of cardinality n+1 with norm ? satisfying the condition maxD / minD = 2/ d(X,l8n) for D := { ?(a,b) : a, b ? S, a ? b } can be isometrically embedded into X.