CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

On Nearly Equilateral Simplices and Nearly l Spaces

  Published:2010-05-11
 Printed: Sep 2010
  • Gennadiy Averkov,
    Institute for Mathematical Optimization, Faculty of Mathematics, University of Magdeburg, Magdeburg, Germany
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax  

Abstract

By $\textrm{d}(X,Y)$ we denote the (multiplicative) Banach--Mazur distance between two normed spaces $X$ and $Y.$ Let $X$ be an $n$-dimensional normed space with $\textrm{d}(X,\ell_\infty^n) \le 2,$ where $\ell_\infty^n$ stands for $\mathbb{R}^n$ endowed with the norm $\|(x_1,\dots,x_n)\|_\infty := \max \{|x_1|,\dots, |x_n| \}.$ Then every metric space $(S,\rho)$ of cardinality $n+1$ with norm $\rho$ satisfying the condition $\max D / \min D \le 2/ \textrm{d}(X,\ell_\infty^n)$ for $D:=\{ \rho(a,b) : a, b \in S, \ a \ne b\}$ can be isometrically embedded into $X.$
MSC Classifications: 52A21, 51F99, 52C99 show english descriptions Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
None of the above, but in this section
None of the above, but in this section
52A21 - Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
51F99 - None of the above, but in this section
52C99 - None of the above, but in this section
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/