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Uniqueness of the trace and simplicity

Author: Gerard J. Murphy
Journal: Proc. Amer. Math. Soc. 128 (2000), 3563-3570
MSC (2000): Primary 46L05; Secondary 46L55
Published electronically: June 7, 2000
MathSciNet review: 1707157
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Abstract: It is proved that for certain large classes of unital C*-algebras, the existence of a unique, faithful tracial state implies simplicity. An example is given to show that this implication does not hold for all unital C*-algebras.

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Additional Information

Gerard J. Murphy
Affiliation: Department of Mathematics, University College, Cork, Ireland

Keywords: Faithful tracial state, simple C*-algebra
Received by editor(s): June 29, 1998
Received by editor(s) in revised form: February 2, 1999
Published electronically: June 7, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society