We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators and sequences which are hypercyclic in a weaker sense are shown. Our results extend and improve a result on denseness due to C. Kitai.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-7,
author = {Luis Bernal-Gonzalez},
title = {Dense range perturbations of hypercyclic operators},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {283-292},
zbl = {1006.47007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-7}
}
Luis Bernal-Gonzalez. Dense range perturbations of hypercyclic operators. Colloquium Mathematicae, Tome 91 (2002) pp. 283-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-7/