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Coarse embeddings of metric spaces into Banach spaces

Piotr W. Nowak
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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 $L_p(μ)$, 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.

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Piotr W. Nowak. 2004-04-22. Coarse embeddings of metric spaces into Banach spaces. https://arxiv.org/abs/math/0404401

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