Skip to main content
SpringerLink
Log in

On mixing properties of automorphisms of von neumann algebras related to measure space transformations

  • Conference paper
  • First Online:
Quantum Probability and Applications III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1303))

  • 519 Accesses

Abstract

The mixing properties of shift-automorphisms of an infinite tensor product of matrix algebras with a shift invariant (but, in general, non-product) state are studied. It is shown that if the centralizer of the von Neumann algebra is a type II1 factor, then the mixing properties of the shift automorphism correspond to the mixing properties of the underlying measure space shift.

Work finished during a visit at the Institut für Theoretische Physik der Universität Wien.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Connes, A.: Une classification des facteurs de type III, Ann. Sci. Ec. Norm. Sup. 6 (1973) p. 133. 252.

    MathSciNet  MATH  Google Scholar 

  2. Connes, A. and Størmer, E.: Entropy for automorphisms of II1 von Neumann Algebras, Acta Math. 134 (1975) p. 289–306.

    Article  MathSciNet  MATH  Google Scholar 

  3. Denker, M., Grillenberger, Ch. and Sigmund, K.: Ergodic Theory on Compact Sets, Springer Lecture Notes in Math. 527, 1976.

    Google Scholar 

  4. Krieger, W.: On non-singular transformations of a measure space I, Zeitschrift für Wahrscheinlichkeitstheorie u. verw. Geb. 11 (1969) p. 83–97.

    Article  MathSciNet  MATH  Google Scholar 

  5. Krieger, W.: On the finitary isomorhisms of Markov shifts that have finite expected coding time, Zeitschrift für Wahrscheinlichkeitstheorie u. verw. Geb. 65 (1983) p. 323–328.

    Article  MathSciNet  MATH  Google Scholar 

  6. Quasthoff, U.: Shift automorphisms of the hyperfinite factor, Math. Nachrichten 131 (1987) p. 101–106.

    Article  MathSciNet  MATH  Google Scholar 

  7. Quasthoff, U.: On autmorphisms of factors related to measure space transformations, in preparation.

    Google Scholar 

  8. Ruelle, D.: Statistical Mechanics, Benjamin, New York, 1969.

    MATH  Google Scholar 

  9. Schröder, W.: W*-K-Systems, Thesis, Tübingen 1983.

    Google Scholar 

  10. Walters, P.: An Introduction to Ergodic Theory, Springer 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karl-Marx-Universität Leipzig Sektion Mathematik, DDR-7010, Leipzig

    Uwe Quasthoff

Authors
  1. Uwe Quasthoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Luigi Accardi Wilhelm von Waldenfels

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Quasthoff, U. (1988). On mixing properties of automorphisms of von neumann algebras related to measure space transformations. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications III. Lecture Notes in Mathematics, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078069

Download citation

  • DOI: https://doi.org/10.1007/BFb0078069

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18919-0

  • Online ISBN: 978-3-540-38846-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation