The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space

The Coarse Baum – Connes Conjecture for Spaces Which Admit a Uniform Embedding into Hilbert Space

Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space

The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infinite locally finite graphs excluding a minor embed coarsely into a Hilbert space. In an appendix a direct proof of the latter result is given. 2000 Mathematics Subject Classification: Primary: 46B20; Sec...

On Embedding of Finite Metric Spaces into Hilbert Space

Metric embedding plays an important role in a vast range of application areas such as computer vision, computational biology, machine learning, networking, statistics, and mathematical psychology, to name a few. The main criteria for the quality of an embedding is its average distortion over all pairs. A celebrated theorem of Bourgain states that every finite metric space on n points embeds in ...

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...

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...