On coarse embeddability into ${\ell }_p$-spaces and a conjecture of Dranishnikov

Abstract

We show that the Hilbert space is coarsely embeddable into any ${\ell }_p$ for $1\le p<\infty$. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space.

5 pages

Cited by in corpus (5)

• The coarse geometry of Tsirelson's space and applications
• A new coarsely rigid class of Banach spaces
• Embeddability of snowflaked metrics with applications to the nonlinear geometry of the spaces $L_p$ and ${\ell }_p$ for $0<p<\infty$
• Quantitative nonlinear embeddings into Lebesgue sequence spaces
• Coarse and uniform embeddings between Orlicz sequence spaces