We study commutants modulo some normed ideal of -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 *-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.
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Dan-Virgil Voiculescu, Countable degree-1 saturation of certain *-algebras which are coronas of Banach algebras. Groups Geom. Dyn. 8 (2014), no. 3, pp. 985–1006DOI 10.4171/GGD/254