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Faber-hypercyclic operators

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Abstract

Let Ω be a bounded domain of the complex plane whose boundary is a closed Jordan curve and (F n ) n≥0 the sequence of Faber polynomials of Ω. We say that a bounded linear operator T on a separable Banach space X is Ω-hypercyclic if there exists a vector x of X such that {F n (T)x: n ≥ 0} is dense in X. We show that many of the results in the spectral theory of hypercyclic operators involving the unit disk or its boundary have Ω-hypercyclic counterparts which involve the domain Ω or its boundary. The influence of the geometry of Ω or the smoothness of its boundary on Faber-hypercyclicity is also discussed.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, UMR 8524, Université des Sciences et Technologies de Lille, Cité Scientifique, 59655, Villeneuve d’Ascq Cedex, France

    Catalin Badea & Sophie Grivaux

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  1. Catalin Badea
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  2. Sophie Grivaux
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Correspondence to Catalin Badea.

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Badea, C., Grivaux, S. Faber-hypercyclic operators. Isr. J. Math. 165, 43–65 (2008). https://doi.org/10.1007/s11856-008-1003-4

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  • DOI: https://doi.org/10.1007/s11856-008-1003-4

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