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 affine isometric action on a direct sum of l p(ℕ) spaces.
All Science Journal Classification (ASJC) codes
- Applied Mathematics