Существование гиперциклических подпространств у операторов Тёплица

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    Abstract

    In this work we construct a class of coanalytic Toeplitz operators, which have an infinitedimensional closed subspace, where any non-zero vector is hypercyclic. Namely, if for a function ϕ which is analytic in the open unit disc D and continuous in its closure the conditions ϕ(T)∩T ≠ ∅ and ϕ(D)∩T ≠ 0 are satisfied, then the operator ϕ(S*) (where S* is the backward shift operator in the Hardy space) has the required property. The proof is based on an application of a theorem by Gonzalez, Leon-Saavedra and Montes-Rodriguez.

    Original languageRussian
    Pages (from-to)102-105
    Number of pages4
    JournalUfa Mathematical Journal
    Volume7
    Issue number2
    DOIs
    StatePublished - 1 Jan 2015

    Scopus subject areas

    • Mathematics(all)

    Keywords

    • Essential spectrum
    • Hardy space
    • Hypercyclic operators
    • Toeplitz operators

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