  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 Herv\'e 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.
