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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Entropy for $ C^*$-algebras with tracial rank zero


Author: Rui Okayasu
Journal: Proc. Amer. Math. Soc. 138 (2010), 3609-3621
MSC (2010): Primary 46L55; Secondary 28D20, 46L40
Published electronically: May 7, 2010
MathSciNet review: 2661560
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Abstract: Voiculescu's topological approximation entropy is extended to automorphisms on unital simple $ C^*$-algebras with tracial rank zero. Several expected properties are shown. We also consider the value of our entropy for a cat map on the non-commutative torus.


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Additional Information

Rui Okayasu
Affiliation: Department of Mathematics Education, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
Email: rui@cc.osaka-kyoiku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10475-4
PII: S 0002-9939(10)10475-4
Keywords: $C^*$-algebras, entropy, trace
Received by editor(s): March 4, 2009
Received by editor(s) in revised form: December 1, 2009, and January 8, 2010
Published electronically: May 7, 2010
Additional Notes: The author was supported in part by the Japan Society for the Promotion of Science
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society