Coarse embeddings of metric spaces into Banach spaces
| dc.creator | Nowak, Piotr W. | |
| dc.date | 2004-04-22 | |
| dc.date.accessioned | 2026-07-07T05:07:38Z | |
| dc.date.available | 2026-07-07T05:07:38Z | |
| dc.description | 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 $L_p(μ)$, 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 $L_p(μ)$, $0<p<2$, the range of spaces, coarse embedding into which guarantees for a finitely generated group $Γ$ to satisfy the Novikov Conjecture. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404401 | |
| dc.identifier | http://arxiv.org/abs/math/0404401 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70934 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 46C05; 46T99 | |
| dc.title | Coarse embeddings of metric spaces into Banach spaces | |
| dc.type | text |