Skip to main content
Log in

Eigenvalues of Weighted Composition Operators on the Bloch Space

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

Abstract

This note discusses eigenvalues of weighted composition operators uC φ on the Bloch space. The main result provides a class of uC φ for which computation of eigenvalues is possible. We also construct an example of a non-compact operator C φ whose eigenvalues can be determined precisely.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hammond, C.: On the norm of a composition operator. PhD dissertation presented at the Graduate Faculty of the University of Virginia (2003) (http://oak.conncoll.edu/cnham)

  2. Madigan K., Matheson A.: Compact composition operators on Bloch spaces. Trans. Am. Math. Soc. 347, 2679–2687 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ohno S., Zhao R.: Weighted composition operators on the Bloch space. Bull. Austral. Math. Soc. 63(2), 177–185 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Shapiro J.: Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer, New York (1993)

    Google Scholar 

  5. Shapiro J., Smith W., Stegenga D.: Geometric models and compactness of composition operators. J. Funct. Anal. 127(1), 21–62 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhu K.: Operator Theory in Function Spaces. Marcel-Deker, New York (1990)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Quang Dieu Nguyen.

Additional information

The authors are partially supported by the Korean Research Foundation Grant KRF-2005-070-C00007. The first author is also partially supported by KRF-2008-314-C00012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hosokawa, T., Nguyen, Q.D. Eigenvalues of Weighted Composition Operators on the Bloch Space. Integr. Equ. Oper. Theory 66, 553–564 (2010). https://doi.org/10.1007/s00020-010-1764-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00020-010-1764-0

Mathematics Subject Classification (2000)

Keywords

Navigation