Skip to main content
Journal of Inequalities and Applications
Download PDF
  • Research Article
  • Open access
  • Published:

Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball

Journal of Inequalities and Applications volume 2007, Article number: 061313 (2007) Cite this article

Abstract

Let be the unit ball in the-dimensional complex space, for, a holomorphic function in, and, a holomorphic map from into itself, the weighted composition operator on the weighted Hardy space is given by, where. This paper discusses the spectrum of when it is compact on a certain class of weighted Hardy spaces and when the composition map has only one fixed point inside the unit ball.

[123456]

References

  1. Cowen CC, MacCluer BD: Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, Fla, USA; 1995:xii+388.

    Google Scholar 

  2. Gunatillake G: Spectrum of a compact weighted composition operator. Proceedings of the American Mathematical Society 2007,135(2):461–467. 10.1090/S0002-9939-06-08497-8

    Article  MathSciNet  MATH  Google Scholar 

  3. Aron R, Lindström M: Spectra of weighted composition operators on weighted banach spaces of analytic functions. Israel Journal of Mathematics 2004, 141: 263–276. 10.1007/BF02772223

    Article  MathSciNet  MATH  Google Scholar 

  4. Clahane DD: Spectra of compact composition operators over bounded symmetric domains. Integral Equations and Operator Theory 2005,51(1):41–56. 10.1007/s00020-003-1250-z

    Article  MathSciNet  MATH  Google Scholar 

  5. MacCluer BD, Weir RJ: Linear-fractional composition operators in several variables. Integral Equations and Operator Theory 2005,53(3):373–402. 10.1007/s00020-005-1372-6

    Article  MathSciNet  MATH  Google Scholar 

  6. Cowen CC, MacCluer BD: Linear fractional maps of the ball and their composition operators. Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 2000,66(1–2):351–376.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300072, China

    Ze-Hua Zhou & Cheng Yuan

Authors
  1. Ze-Hua Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheng Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ze-Hua Zhou.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Zhou, ZH., Yuan, C. Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball. J Inequal Appl 2007, 061313 (2007). https://doi.org/10.1155/2007/61313

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/61313

Keywords