## Coarse embeddings of metric spaces into Banach spaces

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- by Piotr W. Nowak PDF
- Proc. Amer. Math. Soc.
**133**(2005), 2589-2596 Request permission

## 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.## References

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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
- Received by editor(s): October 5, 2003
- Published electronically: April 19, 2005
- Communicated by: Jonathan M. Borwein
- © Copyright 2005 American Mathematical Society
- 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
- MathSciNet review: 2146202