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# Irreducible Representations of Inner Quasidiagonal $C^*$-Algebras

Published:2011-04-27
Printed: Sep 2011
Department of Mathematics, University of Nevada, Reno, Reno, NV, U.S.A.
• Eberhard Kirchberg,
Institut für Mathematik, Humboldt Universität zu Berlin, Berlin, Germany
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## 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