Groups, Geometry, and Dynamics
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Published online: 2014-10-02
Countable degree-1 saturation of certain $C$*-algebras which are coronas of Banach algebrasDan-Virgil Voiculescu (1) University of California, Berkeley, United States
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.
Keywords: Countable degree-1 saturation, symmetrically normed ideal, Calkin algebra, quasicentral approximate unit, bidual Banach algebra
Voiculescu Dan-Virgil: Countable degree-1 saturation of certain $C$*-algebras which are coronas of Banach algebras. Groups Geom. Dyn. 8 (2014), 985-1006. doi: 10.4171/GGD/254