Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-20T22:00:54.829Z Has data issue: false hasContentIssue false
  • English
  • Français

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: a.skalski@lancaster.ac.uk)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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