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Coarse embeddings of metric spaces into Banach spaces

Author: Piotr W. Nowak
Journal: Proc. Amer. Math. Soc. 133 (2005), 2589-2596
MSC (2000): Primary 46C05; Secondary 46T99
Published electronically: April 19, 2005
MathSciNet review: 2146202
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Abstract: There are several characterizations of coarse embeddability of locally finite metric spaces 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 us to extend to $L_p(\mu )$, $0<p\le 2$, the range of spaces, coarse embeddings into which is guaranteed for a finitely generated group $\Gamma$ to satisfy the Novikov Conjecture.

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Additional Information

Piotr W. Nowak
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland – and – Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118
Address at time of publication: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240

Keywords: Coarse embeddings, metric spaces, Novikov Conjecture
Received by editor(s): October 5, 2003
Published electronically: April 19, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society