Quantitative K-theory for Banach algebras

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 $L_p$ spaces. We also prove the existence of a controlled Mayer–Vietoris sequence in this framework.