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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 estimates for some C$^*$-endomorphisms


Author: Valentin Deaconu
Journal: Proc. Amer. Math. Soc. 127 (1999), 3653-3658
MSC (1991): Primary 46L55, 28D20
Published electronically: May 17, 1999
MathSciNet review: 1632272
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Abstract: In this paper we compute the non-commutative topological entropy in the sense of Voiculescu for some endomorphisms of stationary inductive limits of circle algebras. These algebras are groupoid C*-algebras, and the endomorphisms restricted to the canonical diagonal are induced by some expansive maps, whose entropies provide a lower bound. For the upper bound, we use a result of Voiculescu, similar to the classical Kolmogorov-Sinai theorem. The same technique is used to compute the entropy of a non-commutative Markov shift.


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Additional Information

Valentin Deaconu
Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557
Email: vdeaconu@math.unr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05090-X
PII: S 0002-9939(99)05090-X
Received by editor(s): February 20, 1998
Published electronically: May 17, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society