Skip to main content
SpringerLink
Log in

Asymptotic T u -Toeplitzness of weighted composition operators on H2

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

Given a unilateral forward shift S acting on a complex, separable, innite dimensional Hilbert space H, an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that {S*nTSn} is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H. In this paper, we study the asymptotic T u -Toeplitzness of weighted composition operators on the Hardy space H2, where u is a nonconstant inner function.

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. Barría J, Halmos P R. Asymptotic Toeplitz operators. Trans Amer Math Soc, 1982, 273: 621–630

    Article  MathSciNet  MATH  Google Scholar 

  2. Bourdon P, Narayan S K. Normal weighted composition operators on the Hardy space H 2(D). J Math Anal Appl, 2010, 367: 278–286

    Article  MathSciNet  MATH  Google Scholar 

  3. Coburn L A. The C*-algebra generated by an isometry, II. Trans Amer Math Soc, 1969, 137: 211–217

    MathSciNet  MATH  Google Scholar 

  4. Cowen C C. Composition operators on H 2. J Operator Theory, 1983, 9: 77–106

    MathSciNet  MATH  Google Scholar 

  5. Cowen C C. Linear fractional composition operators on H 2. Integral Equations Operator Theory, 1988, 11: 151–160

    Article  MathSciNet  MATH  Google Scholar 

  6. Cowen C C, Jung S, Ko E. Normal and cohyponormal weighted composition operators on H 2. Oper Theory Adv Appl, 2014, 240: 69–85

    Article  MATH  Google Scholar 

  7. Cowen C C, Ko E. Hermitian weighted composition operator on H 2. Trans Amer Math Soc, 2010, 362: 5771–5801

    Article  MathSciNet  MATH  Google Scholar 

  8. Cowen C C, Kriete T L. Subnormality and composition operators on H 2. J Funct Anal, 1988, 81: 298–319

    Article  MathSciNet  MATH  Google Scholar 

  9. Cowen C C, MacCluer B D. Composition Operators on Spaces of Analytic Functions. Boca Raton: CRC Press, 1995

    MATH  Google Scholar 

  10. Cuckovic Z, Nikpour M. On the Toeplitzness of the adjoint of composition operators. J Math Anal Appl, 2013, 408: 541–546

    Article  MathSciNet  MATH  Google Scholar 

  11. Duna C, Gagne M, Gu C, et al. Toeplitzness of products of composition operators and their adjoints. J Math Anal Appl, 2014, 410: 577–584

    Article  MathSciNet  MATH  Google Scholar 

  12. Fatehi M, Robati K. Essential normality for certain weighted composition operators on the Hardy space H 2. Turkish J Math, 2012, 36: 583–595

    MathSciNet  MATH  Google Scholar 

  13. Feintuch A. On asymptotic Toeplitz and Hankel operators. Oper Theory Adv Appl, 1989, 41: 241–254

    MathSciNet  MATH  Google Scholar 

  14. Gunatillake G. Weighted composition operators. PhD Thesis. West Lafayette: Purdue University, 1992

    MATH  Google Scholar 

  15. Jung S, Ko E. Self-commutators of invertible weighted composition operators on H 2. Complex Var Elliptic Equ, 2014, 59: 693–705

    Article  MathSciNet  MATH  Google Scholar 

  16. Jung S, Ko E. On Tu-Toeplitzness of weighted composition operators on H 2. Complex Var Elliptic Equ, 2015, 60: 1522–1538

    Article  MathSciNet  MATH  Google Scholar 

  17. Matache V. S-Toeplitz composition operators. In: Complex and Harmonic Analysis. Lancaster: DEStech Publ, 2007, 189–204

    Google Scholar 

  18. Matache V. Weighted composition operators on H 2 and applications. Complex Anal Oper Theory, 2008, 2: 169–197

    Article  MathSciNet  MATH  Google Scholar 

  19. Matache V. Invariant subspaces of composition operators. J Operator Theory, 2015, 73: 243–264

    Article  MathSciNet  MATH  Google Scholar 

  20. Nazarov F, Shapiro J H. On the Toeplitzness of composition operators. Complex Var Elliptic Equ, 2007, 52: 193–210

    Article  MathSciNet  MATH  Google Scholar 

  21. Rosenblum M, Rovnyak J. Hardy Classes and Operator Theory. Oxford: Oxford University Press, 1985

    MATH  Google Scholar 

  22. Shapiro J H. Composition Operators and Classical Function Theory. New York: Springer-Verlag, 1993

    Book  MATH  Google Scholar 

  23. Sung J, Kim Y, Ko E. Characterizations of binormal composition operators on H 2. Appl Math Comput, 2015, 261: 252–263

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by Hankuk University of Foreign Studies Research Fund.

Author information

Authors and Affiliations

  1. Department of Mathematics, Hankuk University of Foreign Studies, Yongin, 17035, Korea

    Sungeun Jung

Authors
  1. Sungeun Jung
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sungeun Jung.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jung, S. Asymptotic T u -Toeplitzness of weighted composition operators on H2. Sci. China Math. 61, 881–896 (2018). https://doi.org/10.1007/s11425-017-9110-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-017-9110-7

Keywords

MSC(2010)

Search

Navigation