Skip to main content
SpringerLink
Log in

Uniformly ergodic maps onC*-algebras 027

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

LetT be an identity preserving Schwarz map on aC *-algebra. The following conditions are proved to be equivalent: (a)T is uniformly ergodic with finite-dimensional fixed space. (b)T is quasi-compact.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M.-D. Choi,A Schwarz inequality for positive linear maps on C *-algebra, Ill. J. Math.18 (1974), 565–574.

    MATH  Google Scholar 

  2. R. Derndinger, R. Nagel and G. Palm,13 Lectures on Ergodic Theory, preprint, Tübingen, 1982.

  3. N. Dunford and J. T. Schwartz,Linear Operators: Part I: General Theory, Wiley, New York, 1958.

    Google Scholar 

  4. U. Groh,The peripheral point spectrum of Schwarz operator on C *-algebras, Math. Z.176 (1981), 311–318.

    Article  MATH  MathSciNet  Google Scholar 

  5. U. Groh,Uniform ergodic theorems for identity preserving Schwarz maps on W *-algebras, J. Operator Theory, to appear.

  6. B. Kümmerer and R. Nagel,Mean ergodic semigroups on W *-algebras, Acta Sci. Math.41 (1979), 151–159.

    MATH  Google Scholar 

  7. M. Lin,On the uniform ergodic theorem, Proc. Am. Math. Soc.43 (1974), 337–340.

    Article  MATH  Google Scholar 

  8. M. Lin,Quasi-compactness and uniform ergodicity of Markov operators, Ann. Inst. Henri Poincaré11 (1975), 345–354.

    Google Scholar 

  9. M. Lin,Quasi-compactness and uniform ergodicity of positive operators, Isr. J. Math.29 (1978), 309–311.

    Article  MATH  Google Scholar 

  10. H. P. Lotz,Quasi-compactness and uniform ergodicity of Markov operators on C(X), Math. Z.178 (1981), 145–156.

    Article  MathSciNet  Google Scholar 

  11. H. H. Schaefer,Banach Lattices and Positive Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1974.

    MATH  Google Scholar 

  12. E. Størmer,Positive linear maps on operator algebras, Acta Math.110 (1963), 233–278.

    Article  MATH  MathSciNet  Google Scholar 

  13. S. Stratila and L. Zsido,Lectures on von Neumann Algebras, Abacus Press, Tunbridge Wells, Kent, 1979.

    MATH  Google Scholar 

  14. M. Takesaki,Theory of Operator Algebras I, Springer-Verlag, New York-Heidelberg-Berlin 1979.

    MATH  Google Scholar 

  15. K. Yosida,Functional Analysis, 4th edn., Springer-Verlag, Berlin-Heidelberg-New York, 1974.

    MATH  Google Scholar 

  16. K. Yosida and S. Kakutani,Operator theoretical treatment of Markov process and mean ergodic theorem, Ann. of Math.42 (1941), 188–228.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 74, Tübingen, FRG

    Ulrich Groh

Authors
  1. Ulrich Groh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Groh, U. Uniformly ergodic maps onC*-algebras 027. Israel J. Math. 47, 227–235 (1984). https://doi.org/10.1007/BF02760517

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760517

Keywords

Search

Navigation