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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-3-1,
author = {George Costakis},
title = {Common Ces\`aro hypercyclic vectors},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {203-226},
zbl = {1206.47011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-3-1}
}
George Costakis. Common Cesàro hypercyclic vectors. Studia Mathematica, Tome 196 (2010) pp. 203-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-3-1/