Skip to main content
SpringerLink
Log in

Compact Sums of Toeplitz Products on Weighted Bergman and Dirichlet Spaces

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

On the weighted Bergman and Dirichlet spaces, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Our results extend the several known results by using complete different arguments.

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. Adams, R.: Sobolev Spaces. Academic, New York (1975)

    MATH  Google Scholar 

  2. Axler, S., Zheng, D.: Compact operators via the Berezin transform. Indiana Univ. Math. J. 47, 387–400 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lu, Y., Hu, Y., Liu, L.: Compact Toeplitz operators on the weighted Dirichlet space. Acta Mathematica Sinica 31, 35–43 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lee, Y.J., Zhu, K.: Sums of products of Toeplitz and Hankel operators on the Dirichlet space. Integral Equ. Oper. Theory 71, 275–302 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Nakazi, T., Yoneda, R.: Compact Toeplitz operators with continuous symbols on weighted Bergman spaces. Glasgow Math. J. 42, 31–35 (2000)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the referee for many helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics, Chonnam National University, Gwangju, 500-757, South Korea

    Young Joo Lee

  2. King Jeongjo College of Liberal Arts, Mathematics, Hanshin University, Osan, Gyeonggi, 447-791, South Korea

    Kyunguk Na

Authors
  1. Young Joo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kyunguk Na
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kyunguk Na.

Additional information

Communicated by Terhorst, Dmitry, Izchak and Alpay.

The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A4A01003810). Also, the second author was supported by Hanshin University Research Grant.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, Y.J., Na, K. Compact Sums of Toeplitz Products on Weighted Bergman and Dirichlet Spaces. Complex Anal. Oper. Theory 10, 1799–1809 (2016). https://doi.org/10.1007/s11785-016-0576-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11785-016-0576-x

Keywords

Mathematics Subject Classification

Search

Navigation