Concentration of the distance in finite dimensional normed spaces

被引：23

作者：

Arias-De-Reyna, J

Ball, K

Villa, R

机构：

[1] Univ Seville, Fac Matemat, Dept Anal Matemat, E-41012 Seville, Spain

[2] UCL, Dept Math, London WC1E 6BT, England

来源：

MATHEMATIKA | 1998年 / 45卷 / 90期

关键词：

D O I：

10.1112/S0025579300014182

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that in every finite dimensional normed space, for "most" pairs (x, y) of points in the unit ball, \\x-v\\ is more than root 2(1 - epsilon). 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 root 2(1 - epsilon).

引用

页码：245 / 252

页数：8

共 50 条

[41] ON THE EXISTENCE OF MASS MINIMIZING RECTIFIABLE G CHAINS IN FINITE DIMENSIONAL NORMED SPACES
DE Pauw, Thierry
Vasilyev, Ioann
[J]. ANNALES DE L INSTITUT FOURIER, 2023, 73 (02) : 635 - 694
[42] Global versus local asymptotic theories of finite-dimensional normed spaces
Milman, VD
Schechtman, G
[J]. DUKE MATHEMATICAL JOURNAL, 1997, 90 (01) : 73 - 93
[43] Sufficient enlargements of minimal volume for finite-dimensional normed linear spaces
Ostrovskii, M. I.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (03) : 589 - 619
[44] THE COTYPE CONSTANT AND AN ALMOST EUCLIDEAN DECOMPOSITION FOR FINITE-DIMENSIONAL NORMED SPACES
DILWORTH, S
SZAREK, S
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1985, 52 (1-2) : 82 - 96
[45] HYPERPLANES OF FINITE-DIMENSIONAL NORMED SPACES WITH THE MAXIMAL RELATIVE PROJECTION CONSTANT
Kobos, Tomasz
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 91 (03) : 447 - 463
[46] SOME NORM-NORMAL OPERATORS IN FINITE-DIMENSIONAL NORMED SPACES
DEUTSCH, E
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1974, 8 (OCT): : 664 - 666
[47] ALMOST EUCLIDEAN QUOTIENT-SPACES OF SUBSPACES OF A FINITE-DIMENSIONAL NORMED SPACE
MILMAN, VD
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 94 (03) : 445 - 449
[48] D-boundedness and D-compactness in finite dimensional probabilistic normed spaces
Saadati, R
Amini, M
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2005, 115 (04): : 483 - 492
[49] On Lipschitz retraction of finite subsets of normed spaces
Earnest Akofor
[J]. Israel Journal of Mathematics, 2019, 234 : 777 - 808
[50] D-boundedness andD-compactness in finite dimensional probabilistic normed spaces
Reza Saadati
Massoud Amini
[J]. Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2005, 115 : 483 - 492

← 1 2 3 4 5 →