Uniform embeddings of bounded geometry spaces into reflexive Banach space

Brown, Nathanial; Guentner, Erik

doi:10.1090/S0002-9939-05-07721-X

Uniform embeddings of bounded geometry spaces into reflexive Banach space
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by Nathanial Brown and Erik Guentner PDF

Proc. Amer. Math. Soc. 133 (2005), 2045-2050 Request permission

Abstract:

We show that every metric space with bounded geometry uniformly embeds into a direct sum of $l^p ({\mathbb N})$ 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 $l^p ({\mathbb N})$ 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 $l^p ({\mathbb N})$ spaces.

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