Geodesic
On Nearly Equilateral Simplices and Nearly l ∞ Spaces
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 394-397

Voir la notice de l'article provenant de la source Cambridge University Press

By $\text{d(X,Y)}$ we denote the (multiplicative) Banach–Mazur distance between two normed spaces $X$ and $Y$ . Let $X$ be an $n$ -dimensional normed space with $\text{d(X,}\,l_{\infty }^{n}\text{)}\,\le \,\text{2}$ , where $l_{\infty }^{n}$ stands for ${{\mathbb{R}}^{n}}$ endowed with the norm $\parallel ({{x}_{1}},\,.\,.\,.\,,\,{{x}_{n}}){{\parallel }_{\infty }}\,:=\,\max \{|{{x}_{1}}|,\,.\,.\,.\,,\,|{{x}_{n}}|\}$ . Then every metric space $(S,\,\rho )$ of cardinality $n+1$ with norm $\rho $ satisfying the condition $\max D/\min D\,\le \,2/\,\text{d(}X,\,l_{\infty }^{n}\text{)}$ for $D\,:=\,\{\rho (a,\,b)\,:\,a,\,b\,\in \,S,\,a\,\ne \,b\}$ can be isometrically embedded into $X$ .
DOI : 10.4153/CMB-2010-055-1
Mots-clés : 52A21, 51F99, 52C99 
Averkov, Gennadiy. On Nearly Equilateral Simplices and Nearly l ∞ Spaces. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 394-397. doi: 10.4153/CMB-2010-055-1
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