Miscellaneous on commutants mod normed ideals and quasicentral modulus $I$

Abstract

We define commutants mod normed ideals associated with compact smooth manifolds with boundary. The results about the $K$-theory of these operator algebras include an exact sequence for the connected sum of manifolds, derived from the Mayer–Vietoris sequence. We also make a few remarks about bicommutants mod normed ideals and about the quasicentral modulus for the quasinormed $p$-Schatten–von Neumann classes 0 < $p$ < 1.