Common Cesàro hypercyclic vectors

• Autorzy: George Costakis
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 201
• Numer: 3
• Strony: 203-226

Daty

wydano

2010

Twórcy

autor

George Costakis

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

Identyfikatory

DOI

10.4064/sm201-3-1