Coarse embeddings into superstable spaces

Coarse and Uniform Embeddings into Reflexive Spaces

Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spac...

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...

Coarse embeddings of locally finite metric spaces into Banach spaces without cotype

M. Gromov [7] suggested to use coarse embeddings into a Hilbert space or into a uniformly convex space as a tool for solving some of the well-known problems. G. Yu [21] and G. Kasparov and G. Yu [11] have shown that this is indeed a very powerful tool. On the other hand, there exist separable metric spaces ([6] and [5, Section 6]) which are not coarsely embeddable into Hilbert spaces. In [9] (s...

Coarse embeddability into Banach spaces

Equivariant Embeddings of Trees into Hyperbolic Spaces

For every cardinal α ≥ 2 there are three complete constant curvature model manifolds of Hilbert dimension α: the sphere S, the Euclidean space E and the hyperbolic space H. Studying isometric actions on these spaces corresponds in the first case to studying orthogonal representations and in the second case to studying cohomology in degree one with orthogonal representations as coefficients. In ...