Skip to main content
Log in

Dynamical approximation entropies and topological entropy in operator algebras

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Dynamical entropy invariants, based on a general approximation approach are introduced for C*-and W*-algebra automorphisms. This includes a noncommutative extension of topological entropy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Choi, M.-D., Effros, E.G.: NuclearC *-algebras and the approximation property. Am. J. Math.100, 61–79 (1978)

    Google Scholar 

  2. Christensen, E.: Subalgebras of finite algebras. Math. Ann.243, 17–29 (1973)

    Google Scholar 

  3. Connes, A., Narnhofer, H., Thirring, W.: Dynamical entropy ofC *-algebras and von Neumann algebras. Commun. Math. Phys.112, 691–719 (1987)

    Google Scholar 

  4. Connes, A., Störmer, E.: Entropy of II1 von Neumann algebras. Acta Math.134, 289–306 (1975)

    Google Scholar 

  5. Hudetz, T.: Topological entropy for appropriately approximatedC *-algebras. Preprint

  6. Kolmogorov, A.N., Tihomirov, B.: ɛ-entropy and ɛ-capacity of sets in functional spaces. Uspekhi Mat. Nauk14, Part 2 (86) 3–86 (1959)

    Google Scholar 

  7. Narnhofer, H.: Dynamical entropy for the quantized cat map. Preprint, February 1993

  8. Peterson, K.: Ergodic Theory. University Press, 1983

  9. Sauvageot, J.-L., Thouvenot, P.: Une nouvelle definition de l'entropie dynamique des systemes non-commutatifs. Commun. Math. Phys.145, 411–423 (1992)

    Google Scholar 

  10. Shannon, C.E., Weaver, W.: The Mathematical Theory of Communications. University of Illinois Press, 1963

  11. Störmer, E.: Entropy in operator algebras. Preprint (1992)

  12. Störmer, E., Voiculescu, D.: Entropy of Bogoliubov automorphisms of the canonical anticommutation relations. Commun. Math. Phys.133, 521–542 (1990)

    Google Scholar 

  13. Thomsen, K.: Topological entropy for endomorphisms of localC *-algebras. Preprint

  14. Voiculescu, D. Alternative entropies in operator algebras. To appear in the Proceedings of the 1992 European Congress of Mathematicians

  15. Narnhofer, H., Störmer, E., Thirring, E.:C *-dynamical systems for which the tensor product formula for entropy fails. Preprint, Summer 1994

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Connes

Supported in part by Grant No. DMS 9204174 from the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voiculescu, D. Dynamical approximation entropies and topological entropy in operator algebras. Commun.Math. Phys. 170, 249–281 (1995). https://doi.org/10.1007/BF02108329

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02108329

Keywords

Navigation