Countable Degree-1 Saturation of Certain C*-Algebras Which Are Coronas of Banach Algebras

Abstract

We study commutants modulo some normed ideal of n-tuples of operators which satisfy a certain approximate unit condition relative to the ideal. We obtain results about the quotient of these Banach algebras by their ideal of compact operators being C*-algebras which have the countable degree-1 saturation property in the model-theory sense of I. Farah and B. Hart. We also obtain results about quasicentral approximate units, multipliers and duality.