An isomorphic Dvoretzky's theorem for convex bodies
Studia Mathematica, Tome 127 (1998) no. 2, pp. 191-200
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that there exist constants C>0 and 0 λ 1 so that for all convex bodies K in $ℝ^n$ with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of $ℝ^n$ satisfying $d(Y ∩ K, B_2^k) ≤ C(1+ √(k/ln(n/(kln(n+1))))$. This formulation of Dvoretzky's theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.
@article{10_4064_sm_127_2_191_200,
author = {Y. Gordon and O. Gu\'edon and M. Meyer},
title = {An isomorphic {Dvoretzky's} theorem for convex bodies},
journal = {Studia Mathematica},
pages = {191--200},
publisher = {mathdoc},
volume = {127},
number = {2},
year = {1998},
doi = {10.4064/sm-127-2-191-200},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-127-2-191-200/}
}
TY - JOUR AU - Y. Gordon AU - O. Guédon AU - M. Meyer TI - An isomorphic Dvoretzky's theorem for convex bodies JO - Studia Mathematica PY - 1998 SP - 191 EP - 200 VL - 127 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-127-2-191-200/ DO - 10.4064/sm-127-2-191-200 LA - en ID - 10_4064_sm_127_2_191_200 ER -
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Y. Gordon; O. Guédon; M. Meyer. An isomorphic Dvoretzky's theorem for convex bodies. Studia Mathematica, Tome 127 (1998) no. 2, pp. 191-200. doi: 10.4064/sm-127-2-191-200
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