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.

**[De]**Valentin Deaconu,*A path model for circle algebras*, J. Operator Theory**34**(1995), no. 1, 57–89. MR**1361567****[Fr]**Shmuel Friedland,*Entropy of graphs, semigroups and groups*, Ergodic theory of 𝑍^{𝑑} actions (Warwick, 1993–1994) London Math. Soc. Lecture Note Ser., vol. 228, Cambridge Univ. Press, Cambridge, 1996, pp. 319–343. MR**1411226**, 10.1017/CBO9780511662812.013**[St]**Erling Størmer,*Entropy in operator algebras*, Astérisque**232**(1995), 211–230. Recent advances in operator algebras (Orléans, 1992). MR**1372535****[Vo]**Dan Voiculescu,*Dynamical approximation entropies and topological entropy in operator algebras*, Comm. Math. Phys.**170**(1995), no. 2, 249–281. MR**1334396****[Wa]**Peter Walters,*An introduction to ergodic theory*, Graduate Texts in Mathematics, vol. 79, Springer-Verlag, New York-Berlin, 1982. MR**648108**

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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

Received by editor(s):
February 20, 1998

Published electronically:
May 17, 1999

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society