Frequently dense orbits |
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Authors: | K.-G. Grosse-Erdmann Alfredo Peris |
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Affiliation: | 1. Fachbereich Mathematik, FernUniversität Hagen, 58084 Hagen, Germany;2. E.T.S. Arquitectura, Departament de Matemàtica Aplicada and IMPA-UPV, Universitat Politècnica de València, 46022 València, Spain |
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Abstract: | We study the notion of frequent hypercyclicity that was recently introduced by Bayart and Grivaux. We show that frequently hypercyclic operators satisfy the Hypercyclicity Criterion, answering a question of Bayart and Grivaux [Trans. Amer. Math. Soc., in press]. We also disprove a conjecture therein concerning frequently hypercyclic weighted shifts, and we prove that vectors which have a somewhere frequently dense orbit are frequently hypercyclic. To cite this article: K.-G. Grosse-Erdmann, A. Peris, C. R. Acad. Sci. Paris, Ser. I 341 (2005). |
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