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Spectra of weighted composition operators on algebras of analytic functions on banach spaces

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Abstract

Let E be a complex Banach space, with the unit ball B E . We study the spectrum of a bounded weighted composition operator u C φ on H ∞(B E ) determined by an analytic symbol φ with a fixed point in B E such that φ(B E ) is a relatively compact subset of E, where u is an analytic function on B E .

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References

  1. R. Aron, M. Lindström: Spectra of weighted composition operators on weighted Banach spaces of analytic functions. Isr. J. Math. 141 (2004), 263–276.

    Article  MATH  Google Scholar 

  2. R. Aron, P. Galindo, M. Lindström: Compact homomorphisms between algebras of analytic functions. Stud. Math. 123 (1997), 235–247.

    MATH  Google Scholar 

  3. J. Bonet, P. Galindo, M. Lindström: Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions. J. Math. Anal. Appl. 340 (2008), 884–891.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Bourdon, J. Shapiro: Mean growth of Königs eigenfunctions. J. Am. Math. Soc. 10 (1997), 299–325.

    Article  MathSciNet  MATH  Google Scholar 

  5. C.C. Cowen, B.D. MacCluer: Spectra of some composition operators. J. Funct. Anal. 125 (1994), 223–251.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Galindo, A. Miralles,: Spectra of non power-compact composition operators on H ∞ spaces. Integral Equations Oper. Theory 65 (2009), 211–222.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Galindo, T.W. Gamelin, M. Lindström: Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets. Trans. Am. Math. Soc. 359 (2007), 2109–2121.

    Article  MATH  Google Scholar 

  8. P. Galindo, T.W. Gamelin, M. Lindström: Spectra of composition operators on algebras of analytic functions on Banach spaces. Proc. R. Soc. Edinb., Sect. A, Math. 139 (2009), 107–121.

    Article  MATH  Google Scholar 

  9. M. Lindström, N. Palmberg: Spectra of composition operators on BMOA. Integral Equations Oper. Theory 53 (2005), 75–86.

    Article  MATH  Google Scholar 

  10. P. Lefèvre: Generalized essential norm of weighted composition operators on some uniform algebras of analytic functions. Integral Equations Oper. Theory 63 (2009), 557–569.

    Article  MATH  Google Scholar 

  11. A.M. Montolío: Algebras de funciones analíticas acotadas. Interpolación. Thesis. Universitat de València, València, 2008.

    Google Scholar 

  12. B. MacCluer, K. Saxe: Spectra of composition operators on the Bloch and Bergman spaces. Isr. J. Math. 128 (2002), 325–354.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Schechter: On the spectra of operators on tensor products. J. Funct. Anal. 4 (1969), 95–99.

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Yuan, Z.-H. Zhou: The essential norm and spectrum of a weighted composition operator on H ∞(B N). Bull. Malays. Math. Sci. Soc 33 (2010), 499–511.

    MathSciNet  MATH  Google Scholar 

  15. L. Zheng: The essential norms and spectra of composition operators on H ∞. Pac. J. Math. 203 (2002), 503–510.

    Article  MATH  Google Scholar 

  16. Z.-H. Zhou, C. Yuan: Spectrum of compact weighted composition operators on the weighted Hardy space in the unit ball. J. Inequal. Appl. (2007), 1–8. Article ID 61313, doi:10.1155/2007/61313.

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Authors and Affiliations

  1. Institute of Mathematics, School of Science, Tianjin University of Technology and Education, Tianjin, 300222, P.R.China

    Cheng Yuan

  2. Department of Mathematics, Tianjin University, Tianjin, 300072, P.R.China

    Ze-Hua Zhou

Authors
  1. Cheng Yuan
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  2. Ze-Hua Zhou
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Correspondence to Ze-Hua Zhou.

Additional information

Supported in part by the National Natural Science Foundation of China (Grants No. 10971153 and 10671141).

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Yuan, C., Zhou, ZH. Spectra of weighted composition operators on algebras of analytic functions on banach spaces. Czech Math J 61, 371–381 (2011). https://doi.org/10.1007/s10587-011-0081-3

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  • DOI: https://doi.org/10.1007/s10587-011-0081-3

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