Common Cesàro hypercyclic vectors

George Costakis ¹

¹ Department of Mathematics University of Crete Knossos Avenue GR-71409 Heraklion, Crete, Greece

Studia Mathematica, Tome 201 (2010) no. 3, pp. 203-226

Résumé

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.

Détail

DOI : 10.4064/sm201-3-1

Keywords: work which seen continuation paper hadjiloucas author studia math establish existence common ces hypercyclic vectors following classes operators multiples backward shift translation operators iii weighted differential operators order first prove version ansaris theorem operators hypercyclic ces hypercyclic simultaneously argument essentially relies baires category theorem addition minimality irrational rotation runges approximation theorem common hypercyclicity universality criterion established sambarino author adv math play important role proofs