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On automorphisms of C*-algebras whose Voiculescu entropy is genuinely non-commutative

Published online by Cambridge University Press:  06 May 2010

ADAM SKALSKI
ADAM SKALSKI*
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK (email: [email protected])
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Abstract

We use the results of Neshveyev and Størmer to show that for a generic shift on a C*-algebra associated with a bitstream the Voiculescu topological entropy is strictly larger that the supremum of topological entropies of its classical subsystems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 3 , June 2011 , pp. 951 - 954
Copyright
Copyright © Cambridge University Press 2010

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References

[1]Brown, N., Dykema, K. and Shlyakhtenko, D.. Topological entropy of free product automorphisms. Acta Math. 189 (2002), 1–35.CrossRefGoogle Scholar
[2]Connes, A., Narnhofer, H. and Thirring, W.. Dynamical entropy of C *-algebras and von Neumann algebras. Comm. Math. Phys. 112(2) (1987), 691–719.CrossRefGoogle Scholar
[3]Golodets, V. Ya. and Neshveyev, S.. Entropy of automorphisms of II 1-factors arising from the dynamical systems theory. J. Funct. Anal. 181(1) (2001), 14–28.CrossRefGoogle Scholar
[4]Golodets, V. Ya. and Størmer, E.. Entropy of C *-dynamical systems generated by bitstreams. Ergod. Th. & Dynam. Sys. 18 (1998), 859–874.CrossRefGoogle Scholar
[5]Haagerup, U. and Størmer, E.. Maximality of entropy in finite von Neumann algebras. Invent. Math. 132 (1998), 433–455.CrossRefGoogle Scholar
[6]Neshveyev, S. and Størmer, E.. The variational principle for a class of asymptotically abelian C *-algebras. Comm. Math. Phys. 215(1) (2000), 177–196.CrossRefGoogle Scholar
[7]Neshveyev, S. and Størmer, E.. Dynamical entropy in operator algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) (A Series of Modern Surveys in Mathematics, 50). Springer, Berlin, 2006.Google Scholar
[8]Narnhofer, H., Størmer, E. and Thirring, W.. C *-dynamical system for which the tensor product formula for entropy fails. Ergod. Th. & Dynam. Sys. 15 (1995), 961–968.CrossRefGoogle Scholar
[9]Skalski, A.. Noncommutative topological entropy of endomorphisms of Cuntz algebras II. Preprint, arXiv: 1002.2276.Google Scholar
[10]Skalski, A. and Zacharias, J.. Noncommutative topological entropy of endomorphisms of Cuntz algebras. Lett. Math. Phys. 86(2–3) (2008), 115–134.CrossRefGoogle Scholar
[11]Voiculescu, D.. Dynamical approximation entropies and topological entropy in operator algebras. Comm. Math. Phys. 170(2) (1995), 249–281.CrossRefGoogle Scholar