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

DOI:
https://doi.org/10.1090/S0002-9939-05-08150-5

Published electronically:
April 19, 2005

MathSciNet review:
2146202

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Abstract | References | Similar Articles | Additional Information

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

Email:
pnowak@math.vanderbilt.edu

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