Skip to main content
×
×
Home

On Nearly Equilateral Simplices and Nearly l Spaces

  • Gennadiy Averkov (a1)
Abstract

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, ) ≤ 2, where stands for ℝ n endowed with the norm ║(x 1, … , xn )║ := max﹛|x 1|, … , |xn |﹜. Then every metric space (S, ρ) of cardinality n + 1 with norm ρ satisfying the condition maxD/minD ≤ 2/ d(X, ) for D := ﹛ρ(a, b) : a, bS, ab﹜ can be isometrically embedded into X.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On Nearly Equilateral Simplices and Nearly l Spaces
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On Nearly Equilateral Simplices and Nearly l Spaces
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On Nearly Equilateral Simplices and Nearly l Spaces
      Available formats
      ×
Copyright
References
Hide All
[1] Averkov, G. and Düvelmeyer, N., Embedding metric spaces into normed spaces and estimates of metric capacity. Monatsh. Math. 152(2007), no. 3, 197206. doi:10.1007/s00605-007-0472-6
[2] Braß, P., On equilateral simplices in normed spaces. Beiträge Algebra Geom. 40(1999), no. 2, 303307.
[3] Dekster, B. V., Simplexes with prescribed edge lengths in Minkowski and Banach spaces. Acta Math. Hungar. 86(2000), no. 4, 343358. doi:10.1023/A:1006727810727
[4] Gluskin, E. D., The diameter of the Minkowski compactum is roughly equal to n. Funktsional. Anal. i Prilozhen. 15(1981), no. 1, 7273.
[5] Indyk, P. and Matoušek, J., Low-distortion embeddings of finite metric spaces. In: Handbook of discrete and computational geometry. Second ed., Chapman and Hall/CRC Press, Boca Raton, FL, 2004, pp. 177196.
[6] Lindenstrauss, J. and Milman, V. D., The local theory of normed spaces and its applications to convexity. In: Handbook of convex geometry, Vol. A, B, North-Holland, Amsterdam, 1993, pp. 11491220.
[7] Matoušek, J., Lectures on discrete geometry. Graduate Texts in Mathematics, 212, Springer-Verlag, New York, 2002.
[8] Munkres, J. R., Elements of algebraic topology. Addison-Wesley, Menlo Park, CA, 1984.
[9] Schoenberg, I. J., Metric spaces and positive definite functions. Trans. Amer. Math. Soc. 44(1938), no. 3, 522536. doi:10.2307/1989894
[10] Swanepoel, K. J. and Villa, R., A lower bound for the equilateral number of normed spaces. Proc. Amer. Math. Soc. 136(2008), no. 1, 127131. doi:10.1090/S0002-9939-07-08916-2
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed