Advertisement

Periodica Mathematica Hungarica

, Volume 63, Issue 2, pp 191–203 | Cite as

On the commutant of asymptotically non-vanishing contractions

  • György Pál GehérEmail author
  • László Kérchy
Article

Abstract

The injectivity of the commutant mapping of asymptotically nonvanishing contractions is examined. We show that this mapping can be injective even in the presence of a non-trivial stable subspace. Various characterizations of injectivity are provided.

Key words and phrases

commutant mapping unitary asymptote contraction 

Mathematics subject classification numbers

47A45 47A15 47B47 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A]
    C. Apostol, Operators quasisimilar to a normal operator, Proc. Amer. Math. Soc., 53 (1975), 104–106.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [Ba]
    C. J. K. Batty, Asymptotic behaviour of semigroups of operators, Functional analysis and operator theory, Banach Center Publications 30, Polish Acad. Sci., Warsaw, 1994, 35–52.Google Scholar
  3. [Bea]
    B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North Holland, Amsterdam, 1988.zbMATHGoogle Scholar
  4. [Ber]
    H. Bercovici, Operator Theory and Arithmetic in H , Amer. Math. Soc., Rhode Island, 1988.zbMATHGoogle Scholar
  5. [BK]
    H. Bercovici and L. Kérchy, Spectral behaviour of C10-contractions, Operator Theory Live, Theta Ser. Adv. Math. 12, Theta, Bucharest, 2010, 17–33.Google Scholar
  6. [DR]
    C. Davis and P. Rosenthal, Solving linear operator equations, Canad. J. Math., 26 (1974), 1384–1389.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [F]
    L. A. Fialkow, A note on the range of the operator XAXXB, Illinois J. Math., 25 (1981), 112–124.MathSciNetGoogle Scholar
  8. [FF]
    C. Foias and A. E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser Verlag, Basel, 1990.zbMATHGoogle Scholar
  9. [K1]
    L. Kérchy, Isometric asymptotes of power bounded operators, Indiana Univ. Math. J., 38 (1989), 173–188.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [K2]
    L. Kérchy, Operators with regular norm-sequences, Acta Sci. Math. (Szeged), 63 (1997), 571–605.MathSciNetzbMATHGoogle Scholar
  11. [K3]
    L. Kérchy, Hyperinvariant subspaces of operators with non-vanishing orbits, Proc. Amer. Math. Soc., 127 (1999), 1363–1370.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [K4]
    L. Kérchy, Generalized Toeplitz operators, Acta Sci. Math. (Szeged), 68 (2002), 373–400.MathSciNetzbMATHGoogle Scholar
  13. [K5]
    L. Kérchy, Cyclic properties and stability of commuting power bounded operators, Acta Sci. Math. (Szeged), 71 (2005), 299–312.MathSciNetzbMATHGoogle Scholar
  14. [K6]
    L. Kérchy, Shift-type invariant subspaces of contractions, J. Funct. Anal., 246 (2007), 281–301.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [KL]
    L. Kérchy and Z. Léka, Representations with regular norm-behaviour of locally compact abelian semigroups, Studia Math., 183 (2007), 143–160.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [KV]
    L. Kérchy and vu Quoc Phong, On invariant subspaces for power-bounded operators of class C1, Taiwanese J. Math., 7 (2003), 69–75.MathSciNetzbMATHGoogle Scholar
  17. [S]
    A. L. Schields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys 13, Amer. Math. Soc., Providence, R. I., 1974, 49–128.Google Scholar
  18. [SzNF]
    B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North Holland — Akadémiai Kiadó, Amsterdam — Budapest, 1970.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary

Personalised recommendations