Geodesic
Countable degree-1 saturation of certain $C$*-algebras which are coronas of Banach algebras
Dan-Virgil Voiculescu1 orcid
1University of California, Berkeley, United States
Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 985-1006

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DOI

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.
DOI : 10.4171/ggd/254
Classification : 46-XX, 47-XX
Mots-clés : Countable degree-1 saturation, symmetrically normed ideal, Calkin algebra, quasicentral approximate unit, bidual Banach algebra

Dan-Virgil Voiculescu  1

1 University of California, Berkeley, United States 
Dan-Virgil Voiculescu. Countable degree-1 saturation of certain $C$*-algebras which are coronas of Banach algebras. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 985-1006. doi: 10.4171/ggd/254
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     title = {Countable degree-1 saturation of certain $C$*-algebras which are coronas of {Banach} algebras},
     journal = {Groups, geometry, and dynamics},
     pages = {985--1006},
     year = {2014},
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     number = {3},
     doi = {10.4171/ggd/254},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/254/}
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