Common Cesàro hypercyclic vectors

Volume 201 / 2010

George Costakis Studia Mathematica 201 (2010), 203-226 MSC: Primary 47A16. DOI: 10.4064/sm201-3-1


In this work, which can be seen as a continuation of a paper by Hadjiloucas and the author [Studia Math. 175 (2006)], we establish the existence of common Cesàro hypercyclic vectors for the following classes of operators: (i) multiples of the backward shift, (ii) translation operators and (iii) weighted differential operators. In order to do so, we first prove a version of Ansari's theorem for operators that are hypercyclic and Cesàro hypercyclic simultaneously; then our argument essentially relies on Baire's category theorem. In addition, the minimality of the irrational rotation, Runge's approximation theorem and a common hypercyclicity-universality criterion established by Sambarino and the author [Adv. Math. 182 (2004)], play an important role in the proofs.


  • George CostakisDepartment of Mathematics
    University of Crete
    Knossos Avenue
    GR-71409 Heraklion, Crete, Greece

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