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Uniform embeddings of bounded geometry spaces into reflexive Banach space
This paper appeared in the Proceedings of the Amer. Math. Society.,
133 (2005), 2045-2050.
Abstract (from the preprint)
We show that every metric space with bounded geometry uniformly embeds
into a direct sum of l-p 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 space.
In the case of discrete groups we prove the analogue of
a-T-menability -- the existence of a metrically proper affine
isometric action on a direct sum of l-p spaces.