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Spectra of Composition Operators on BMOA

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Abstract.

It is shown that if ϕ is a univalent self-map on the unit disk \(\mathbb{D},\) is not an automorphism and has a fixed point in \(\mathbb{D}\) and if the essential spectral radius of the composition operator Cϕ on H2 is different from zero, then the spectrum of Cϕ on BMOA coincides with \(\overline {\mathbb{D}}.\) This answers in the affirmative a conjecture by MacCluer and Saxe.

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Authors and Affiliations

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

    M. Lindström & N. Palmberg

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  1. M. Lindström
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  2. N. Palmberg
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Correspondence to M. Lindström.

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Lindström, M., Palmberg, N. Spectra of Composition Operators on BMOA. Integr. equ. oper. theory 53, 75–86 (2005). https://doi.org/10.1007/s00020-004-1307-7

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  • DOI: https://doi.org/10.1007/s00020-004-1307-7

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