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Irreducible Representations of Inner Quasidiagonal C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Bruce Blackadar  and
Eberhard Kirchberg
Bruce Blackadar
Affiliation:
Department of Mathematics, University of Nevada, Reno, Reno, NV, U.S.A. e-mail: bruceb@unr.edu
Eberhard Kirchberg
Affiliation:
Institut für Mathematik, Humboldt Universität zu Berlin, Berlin, Germany e-mail: kirchbrg@mathematik.hu-berlin.de
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Abstract

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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 $\text{NF}$ 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.

Keywords

46L05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 385 - 395
Copyright
Copyright © Canadian Mathematical Society 2011

References

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