On coarse embeddability into $\ell _p$-spaces and a conjecture of Dranishnikov
Fundamenta Mathematicae 189 (2006), 111-116 MSC: Primary 46C05; Secondary 46T99. DOI: 10.4064/fm189-2-2
We show that the Hilbert space is coarsely embeddable into any $\ell _p$ for $1\le p\le \infty $. It follows that coarse embeddability into $\ell _2$ and into $\ell _p$ are equivalent for $1\le p <2$.