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

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Abstract

We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functionsH ν p ∞ when the symbolφ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA

    R. Aron

  2. Department of Mathematics, Åbo Akademi University, FIN-20500, Åbo, Finland

    M. Lindström

Authors
  1. R. Aron
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  2. M. Lindström
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Correspondence to R. Aron.

Additional information

The research of the second author was partially supported by the Academy of Finland Project No. 51906; the research of this paper was carried out while this author was visiting Kent State University, whose hospitality is acknowledged with thanks.

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Aron, R., Lindström, M. Spectra of weighted composition operators on weighted banach spaces of analytic functions. Isr. J. Math. 141, 263–276 (2004). https://doi.org/10.1007/BF02772223

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  • DOI: https://doi.org/10.1007/BF02772223

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