A sequence (Tₙ) of bounded linear operators between Banach spaces X,Y is said to be hypercyclic if there exists a vector x ∈ X such that the orbit Tₙx is dense in Y. The paper gives a survey of various conditions that imply the hypercyclicity of (Tₙ) and studies relations among them. The particular case of X = Y and mutually commuting operators Tₙ is analyzed. This includes the most interesting cases (Tⁿ) and (λₙTⁿ) where T is a fixed operator and λₙ are complex numbers. We also study when a sequence of operators has a large (either dense or closed infinite-dimensional) manifold consisting of hypercyclic vectors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-1-1,
author = {Fernando Le\'on-Saavedra and Vladim\'\i r M\"uller},
title = {Hypercyclic sequences of operators},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {1-18},
zbl = {1106.47011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-1-1}
}
Fernando León-Saavedra; Vladimír Müller. Hypercyclic sequences of operators. Studia Mathematica, Tome 173 (2006) pp. 1-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-1-1/