Skip to main content
SpringerLink
Log in

The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

For a wide class of radial weights we calculate the essential norm of a weighted composition operator \({uC_\varphi}\) on the weighted Banach spaces of analytic functions in terms of the analytic function \({u \colon \mathbb D \to \mathbb C}\) and the nth power of the analytic selfmap \({\varphi}\) of the open unit disc \({\mathbb D}\) . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.

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. Bierstedt K.D., Bonet J., Taskinen J.: Spaces of holomorphic functions with growth conditions and associated weights. Studia Math. 127(2), 137–168 (1998)

    MATH  MathSciNet  Google Scholar 

  2. Bonet J., Domanski P., Lindström M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Canad. Math. Bull. 42(2), 139–148 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bonet J., Domanski P., Lindström M., Taskinen J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 64(1), 101–118 (1998)

    Article  MATH  Google Scholar 

  4. Montes-Rodriguez A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. (2) 61(3), 872–884 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cowen C., MacCluer B.: Composition operators on spaces of analytic functions. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  6. Shapiro J.H.: Composition operators and classical function theory. Springer, New York (1993)

    MATH  Google Scholar 

  7. Zhao R.: Essential norm of composition operators between Bloch type spaces. Proc. Am. Math. Soc. 138(7), 2537–2546 (2010)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Oulu, 90014, Oulu, Finland

    Olli Hyvärinen, Mika Kemppainen, Mikael Lindström, Antti Rautio & Erno Saukko

Authors
  1. Olli Hyvärinen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mika Kemppainen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mikael Lindström
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Antti Rautio
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Erno Saukko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olli Hyvärinen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hyvärinen, O., Kemppainen, M., Lindström, M. et al. The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions. Integr. Equ. Oper. Theory 72, 151–157 (2012). https://doi.org/10.1007/s00020-011-1919-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00020-011-1919-7

Mathematics Subject Classification (2010)

Keywords

Search

Navigation