Uniform embeddings of bounded geometry spaces into reflexive banach space

摘要

We show that every metric space with bounded geometry uniformly embeds into a direct sum of l(p)( N) spaces ( p's going off to infinity). In particular, every sequence of expanding graphs uniformly embeds into such a reflexive Banach space even though no such sequence uniformly embeds into a fixed l(p)( N) space. In the case of discrete groups we prove the analogue of a-T-menability - the existence of a metrically proper a. ne isometric action on a direct sum of l(p)( N) spaces.