Randomized isomorphic Dvoretzky theorem

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• 作者：Litvak ; Alexander ; Mankiewicz ; Piotr ; Tomczak-Jaegermann ; Nicole
• 刊名：Comptes Rendus Mathematique
• 出版年：2002
• 出版时间：2002
• 年：2002
• 卷：335
• 期：4
• 页码：345-350
• 全文大小：79.2 K

文摘

Let K be a symmetric convex body in R^N for which B₂^N is the ellipsoid of minimal volume. We provide estimates for the geometric distance of a ‘typical’ rank n projection of K to B₂ⁿ, for 1≤n<N. Known examples show that the resulting estimates are optimal (up to numerical constants) even for the Banach–Mazur distance. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 345–350.