Skip to main content

Semigroups in finite von Neumann algebras

  • Conference paper
  • 376 Accesses

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 127))

Abstract

Let M be a finite von Neumann algebra. In the first part, we give asymptotic results about M-stable sequences of weak*-continuous mappings which are related with operators belonging to M. In the second part, we extend, by a shorter way, similarity results given in [CaFa2] to unbounded semigroups of operators contained in a finite von Neumann algebra.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North Holland, Amsterdam, 1988

    Google Scholar 

  2. S. Brown, B. Chevreau and C. Pearcy, Contractions with rich spectrum have invariant subspaces, J. Operator Theory, 1 (1979), 123–136.

    MathSciNet  MATH  Google Scholar 

  3. G. Cassier and T. Face, Contractions in von Neumann algebras, J. Funct. Anal., 135 (1996), 297–338.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Cassier and T. Face, On power-bounded operators in finite von Neumann algebras, J. Funct. Anal., 141 (1996), 133–158.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Dixmier, Les algèbres d’opérateurs dans l’espace Hilbertien (Algèbre de von Neumann),Gauthier-Villards, Paris, 1969.

    MATH  Google Scholar 

  6. J. Dixmier, Les moyennes invariantes dans les semi-groupes et leurs applications, Acta Sci. Math. (Szeged), 12 (1950), 213–227.

    MathSciNet  MATH  Google Scholar 

  7. G. G. Lorentz, A contribution to the theory of divergent sequences, Acta. Math.,80 (1948), 167–190.

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Kérchy, Operators with regular norm sequences, Acta Sci. Math. (Szeged), 63 (1997), 571–605.

    MATH  Google Scholar 

  9. L. Kérchy, Criteria of regularity for norm sequences, Integral Equations Operator Theory, 34 (1999), 458–477.

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Kérchy, Representations with regular norm-behavior of discrete abelian semi-groups, Acta Sci. Math. (Szeged), 65 (1999), 702–726.

    Google Scholar 

  11. L. Kérchy, Hyperinvariant subspaces of operators with non-vanishing orbits, Proc. Amer. Math. Soc., 127 (1999), 1363–1370.

    Article  MathSciNet  MATH  Google Scholar 

  12. L. Kérchy, Unbounded representations of discrete abelian semigroups, Progress in Nonlinear Differential Equations and Their Applications, 42 (2000), 141–150.

    Google Scholar 

  13. L. Kérchy and V. Müller, Criteria of regularity for norm sequences. II,Acta Sci. Math. (Szeged),65 (1999), 131–138.

    MATH  Google Scholar 

  14. S. Sakai, C * algebras and W* algebras, Ergebnisse der Mathematik and ihrer Grenzgebiete 60, Springer-Verlag, Berlin-New York, 1971.

    Book  MATH  Google Scholar 

  15. B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged), 11 (1947), 152–157.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Cassier, G. (2001). Semigroups in finite von Neumann algebras. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds) Recent Advances in Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 127. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8374-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8374-0_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9539-2

  • Online ISBN: 978-3-0348-8374-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics