Groups, Geometry, and Dynamics


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Volume 8, Issue 3, 2014, pp. 985–1006
DOI: 10.4171/GGD/254

Published online: 2014-10-02

Countable degree-1 saturation of certain $C$*-algebras which are coronas of Banach algebras

Dan-Virgil Voiculescu[1]

(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