Quantitative K-theory for Banach algebras

摘要

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 Herve 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 L-p spaces. We also prove the existence of a controlled Mayer-Vietoris sequence in this framework. (C) 2017 Elsevier Inc. All rights reserved.