No abstract

We investigate the rigidity of the ℓp analog of Roe‐type algebras. In particular, we show that if p∈[1,∞)∖{2}, then an isometric isomorphism between the ℓp uniform Roe algebras of two metric spaces with bounded geometry yields a bijective coarse equivalence between the underlying metric spaces, while a stable isometric isomorphism yields a coarse equivalence. We also obtain similar results for other ℓp Roe‐type algebras. In this paper, we do not assume that the metric spaces have Yu's property A or finite decomposition complexity.

Abstract. Quantitative (or controlled) K-theory for C * -algebras was used by Guoliang Yu in his work on the Novikov conjecture, and later developed more formally by Yu together with Hervé Oyono-Oyono. In this paper, we extend their work by developing a framework of quantitative K-theory for the class of algebras of bounded linear operators on subquotients (i.e., subspaces of quotients) of Lp spaces. We also prove the existence of a controlled Mayer-Vietoris sequence in this framework.