Elsevier

Advances in Mathematics

Volume 200, Issue 1, 15 February 2006, Pages 125-135
Advances in Mathematics

Two observations regarding embedding subsets of Euclidean spaces in normed spaces

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Abstract

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 ɛ in Dvoretzky's theorem from order of ɛ2 to order of ɛ (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.

MSC

46B07
52A20

Keywords

Dvoretzky's theorem
Johnson–Lindenstrauss lemma

Cited by (0)

1

Supported by the Israel Science Foundation.