An isomorphic Dvoretzky's theorem for convex bodies

Gordon, Y.; Guédon, O.; Meyer, M.

Gordon, Y. ; Guédon, O. ; Meyer, M.

Studia Mathematica, Tome 129 (1998), p. 191-200 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $d (Y \cap K, B_{2}^{k}) \leq C (1 + \sqrt (k / l n (n / (k l n (n + 1))))$ . 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.

Publié le : 1998-01-01

Zbl 0929.46019

EUDML-ID : urn:eudml:doc:216466

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     author = {Y. Gordon and O. Gu\'edon and M. Meyer},
     title = {An isomorphic Dvoretzky's theorem for convex bodies},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {191-200},
     zbl = {0929.46019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv127i2p191bwm}
}

Gordon, Y.; Guédon, O.; Meyer, M. An isomorphic Dvoretzky's theorem for convex bodies. Studia Mathematica, Tome 129 (1998) pp. 191-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv127i2p191bwm/

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