Spectra of weighted composition operators with automorphic symbols

Olli Hyvärinen, Mikael Lindström*, Ilmari Nieminen, Erno Saukko

*Corresponding author for this work

    Research output: Contribution to journalArticleScientificpeer-review

    30 Citations (Scopus)

    Abstract

    Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).

    Original languageEnglish
    Pages (from-to)1749-1777
    Number of pages29
    JournalJournal of Functional Analysis
    Volume265
    Issue number8
    DOIs
    Publication statusPublished - 15 Oct 2013
    MoE publication typeA1 Journal article-refereed

    Keywords

    • Automorphism
    • Fredholm operator
    • Hardy spaces
    • Spectrum
    • Weighted Banach spaces of H-type
    • Weighted Bergman spaces
    • Weighted composition operator

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