Publishing house / Journals and Serials / Studia Mathematica / All issues

Abstract

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.