This is an announcement for the paper "Coarse embeddings of metric spaces into Hilbert spaces" by Piotr W. Nowak.

Abstract: There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces $L_p(\mu)$, we get their coarse embeddability into a Hilbert space for $0<p<2$. This together with a theorem by Banach and Mazur yields that coarse embeddability into $\ell_2$ and into $L_p(0,1)$ are equivalent when $1 \le p<2$. A theorem by G.Yu and the above allow to extend to $L_p(\mu)$, $0<p<2$, the range of spaces, coarse embedding into which guarantees for a finitely generated group $\Gamma$ %(viewed as a metric space) to satisfy the Novikov Conjecture.

Archive classification: Metric Geometry; Functional Analysis

Mathematics Subject Classification: 46C05; 46T99

Remarks: 8 pages

The source file(s), CoarseembeddingsintoBanachspaces.tex: 25381 bytes, is(are) stored in gzipped form as 0404401.gz with size 8kb. The corresponding postcript file has gzipped size 47kb.

Submitted from: pnowak@math.tulane.edu

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