A lower bound for the equilateral number of normed spaces

Mathematics – Metric Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

5 pages

Scientific paper

10.1090/S0002-9939-07-08916-2

We 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).

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A lower bound for the equilateral number of normed spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A lower bound for the equilateral number of normed spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A lower bound for the equilateral number of normed spaces will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-413610

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.