Common Cesàro hypercyclic vectors

George Costakis. "Common Cesàro hypercyclic vectors." Studia Mathematica 201.3 (2010): 203-226. <http://eudml.org/doc/285433>.

@article{GeorgeCostakis2010,
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.},
author = {George Costakis},
journal = {Studia Mathematica},
language = {eng},
number = {3},
pages = {203-226},
title = {Common Cesàro hypercyclic vectors},
url = {http://eudml.org/doc/285433},
volume = {201},
year = {2010},
}

TY - JOUR
AU - George Costakis
TI - Common Cesàro hypercyclic vectors
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 3
SP - 203
EP - 226
AB - 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.
LA - eng
UR - http://eudml.org/doc/285433
ER -