Abstract view
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Irreducible Representations of Inner Quasidiagonal $C^*$-Algebras
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Published:2011-04-27
Printed: Sep 2011
Bruce Blackadar,
Department of Mathematics, University of Nevada, Reno, Reno, NV, U.S.A.
Eberhard Kirchberg,
Institut für Mathematik, Humboldt Universität zu Berlin, Berlin, Germany
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.
