Connectedness of spectra of toeplitz operators on hardy spaces with muckenhoupt weights over carleson curves

Alexei Yu Karlovich, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Harold Widom proved in 1966 that the spectrum of a Toeplitz operator T(a) acting on the Hardy space Hp(T) over the unit circle T is a connected subset of the complex plane for every bounded measurable symbol a and 1 < p < ∞. In 1972, Ronald Douglas established the connectedness of the essential spectrum of T(a) on H2(T). We show that, as was suspected, these results remain valid in the setting of Hardy spaces Hp(G,&ohgr;),1<p<∞, with general Muckenhoupt weights &ohgr; over arbitrary Carleson curves G.

    Original languageEnglish (US)
    Pages (from-to)83-114
    Number of pages32
    JournalIntegral Equations and Operator Theory
    Volume65
    Issue number1
    DOIs
    StatePublished - Sep 1 2009

    Fingerprint

    Muckenhoupt Weights
    Toeplitz Operator
    Connectedness
    Hardy Space
    Curve
    Essential Spectrum
    Unit circle
    Argand diagram
    Valid
    Subset
    Arbitrary

    Keywords

    • Carleson curve
    • Essential spectrum
    • Hardy space
    • Index
    • Muckenhoupt weight
    • Pettis integral
    • Spectrum
    • Toeplitz operator

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory

    Cite this

    Connectedness of spectra of toeplitz operators on hardy spaces with muckenhoupt weights over carleson curves. / Karlovich, Alexei Yu; Spitkovsky, Ilya.

    In: Integral Equations and Operator Theory, Vol. 65, No. 1, 01.09.2009, p. 83-114.

    Research output: Contribution to journalArticle

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