Ball, KM;
Villa, R;
(1998)
Concentration of the distance between points in the unit ball.
Mathematika
, 45
245 - 252.
10.1112/S0025579300014182.
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Abstract
We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ║x − y║ is more than √2(1 − ε). As a consequence, we obtain a result proved by Bourgain, using QS-decomposition, that guarantees an exponentially large number of points in the unit ball any two of which are separated by more than √2(1 − ε).
| Type: | Article |
|---|---|
| Title: | Concentration of the distance between points in the unit ball |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/S0025579300014182 |
| Publisher version: | http://dx.doi.org/10.1112/S0025579300014182 |
| Language: | English |
| Additional information: | © 1998 Cambridge University Press |
| Keywords: | pure, FUNCTIONAL ANALYSIS, Isometric theory of Banach spaces |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/82460 |
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