Skip to main content
SpringerLink
Log in

Topological structure of the space of composition operators onH ∞

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

Abstract

Components and isolated points of the topological space of composition operators onH ∞ in the uniform operator topology are characterized. Compact differences of two composition operators are also characterized. With the aid of these results, we show that a component inC(H ∞ ) is not in general the set of all composition operators that differ from the given one by a compact operator.

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. E. Berkson, Composition operators isolated in the uniform operator topology,Proc. Amer. Math. Soc. 81 (1981), 230–232.

    Google Scholar 

  2. C. C. Cowen and B. D. MacCluer, “Composition Operators on Spaces of Analytic Functions,” CRC Press, Boca Raton, 1995.

    Google Scholar 

  3. J. Garnett, “Bounded Analytic Functions,” Academic Press, New York, 1981.

    Google Scholar 

  4. B. D. MacCluer, Components in the space of composition operators,Integral Equations Operator Theory 12 (1989), 725–738.

    Google Scholar 

  5. K. Madigan, Composition operators into Lipschitz type spaces, Thesis, SUNY Albany,1993.

  6. J. H. Shapiro and C. Sundberg, Isolation amongst the composition operators,Pacific J. Math. 145 (1990), 117–152.

    Google Scholar 

  7. K. Zhu, “Operator Theory in Function Spaces,” Marcel Dekker, New York, 1990.

    Google Scholar 

  8. K. Zhu, Distances and Banach spaces of holomorphic functions on complex domains,J. London Math. Soc. (2)49 (1994), 163–182.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    Barbara Maccler & Ruhan Zhao

  2. Department of Mathematics, Nippon Institute of Technology, 4-1 Gakuendai, Miyashiro, 345-8501, Minami-Saitama, Japan

    Shûichi Ohno

Authors
  1. Barbara Maccler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shûichi Ohno
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruhan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Grant-in-Aid for Scientific Research (C), the Ministory of Education, Science and Culture, No. 09640218, and the Nippon Institute of Technology No. 111

Supported by the Japan Society for the Promotion of Science

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maccler, B., Ohno, S. & Zhao, R. Topological structure of the space of composition operators onH ∞ . Integr equ oper theory 40, 481–494 (2001). https://doi.org/10.1007/BF01198142

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01198142

1991 Mathematical subject classification

Search

Navigation