Quantitative $K$-theory for $SQ_p$-algebras

Abstract

Quantitative (or controlled) $K$-theory for $C^*$-algebras was introduced by Guoliang Yu in his work on the Novikov conjecture for groups with finite asymptotic dimension, and was later expanded into a general theory, with further applications, by Yu together with Hervé Oyono-Oyono. Motivated by investigations of the $L_p$ Baum-Connes conjecture, we will describe an analogous framework of quantitative $K$-theory that applies to algebras of bounded linear operators on subquotients of $L_p$ spaces