Two observations regarding embedding subsets of Euclidean spaces in normed spaces

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• 作者：Gideon Schechtman
• 关键词：Dvoretzky's theorem ; Johnson– ; Lindenstrauss lemma
• 刊名：Advances in Mathematics
• 出版年：2006
• 出版时间：15 February 2006
• 年：2006
• 卷：200
• 期：1
• 页码：125-135
• 全文大小：159 K

文摘

This paper contains two results concerning linear embeddings of subsets of Euclidean space in low-dimensional normed spaces. The first is an improvement of the known dependence on in Dvoretzky's theorem from order of ² to order of (except for log factors). The second is a joint generalization of (Milman's version of) Dvoretzky's theorem and (a recent generalization by Klartag and Mendelson of) the Johnson–Lindenstrauss Lemma.