Coarse Embeddability Into

Coarse Embeddings of Metric Spaces into Banach Spaces

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 Lp(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 l2 and into L...

On comparison of the coarse embeddability into a Hilbert space and into other Banach spaces

M. Gromov [8] suggested to use uniform embeddings into a Hilbert space or into a uniformly convex space as a tool for solving some of the well-known problems. G. Yu [20] and G. Kasparov and G. Yu [10] have shown that this is indeed a very powerful tool. G. Yu in [20] used the condition of embeddability into a Hilbert space; G. Kasparov and G. Yu [10] used the condition of embeddability into a g...

ON COARSE EMBEDDABILITY INTO lp-SPACES AND A CONJECTURE OF DRANISHNIKOV

We show that the Hilbert space is coarsely embeddable into any lp for 1 ≤ p < ∞. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space. Coarse embeddings were defined by M. Gromov [Gr] to express the idea of inclusion in the large scale geometry of groups. G. Yu showed later that the case when a finitely generated group with a word l...

Coarse embeddability into Banach spaces

Remarks on Quasi-isometric Non-embeddability into Uniformly Convex Banach Spaces

We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...