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Irreducible Representations of Inner Quasidiagonal $C^*$-Algebras |
Canad. Math. Bull. 54(2011), 385-395
Published:2011-04-27
Printed: Sep 2011
Printed: Sep 2011
- Bruce Blackadar,
- Eberhard Kirchberg,
Abstract
It is shown that a separable $C^*$-algebra is inner quasidiagonal if and
only if it has a separating family of quasidiagonal irreducible
representations. As a consequence, a separable $C^*$-algebra is a strong
NF algebra if and only if it is nuclear and has a separating family of
quasidiagonal irreducible representations.
We also obtain some permanence properties of the class of inner
quasidiagonal $C^*$-algebras.
| MSC Classifications: | 46L05 - General theory of $C^*$-algebras |