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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Entropy estimates for some $\mathbf {C}^\ast$-endomorphisms
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by Valentin Deaconu PDF
Proc. Amer. Math. Soc. 127 (1999), 3653-3658 Request permission


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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  • Dan Voiculescu, Dynamical approximation entropies and topological entropy in operator algebras, Comm. Math. Phys. 170 (1995), no. 2, 249–281. MR 1334396
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Additional Information
  • Valentin Deaconu
  • Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557
  • Email:
  • Received by editor(s): February 20, 1998
  • Published electronically: May 17, 1999
  • Communicated by: David R. Larson
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3653-3658
  • MSC (1991): Primary 46L55, 28D20
  • DOI:
  • MathSciNet review: 1632272