Hypercyclic sequences of operators

Fernando León-Saavedra, and Vladimír Müller. "Hypercyclic sequences of operators." Studia Mathematica 175.1 (2006): 1-18. <http://eudml.org/doc/285126>.

@article{FernandoLeón2006,
abstract = {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.},
author = {Fernando León-Saavedra, Vladimír Müller},
journal = {Studia Mathematica},
keywords = {hypercyclic sequence; hypercyclic vector; hypercyclic subspace; essential minimum modulus},
language = {eng},
number = {1},
pages = {1-18},
title = {Hypercyclic sequences of operators},
url = {http://eudml.org/doc/285126},
volume = {175},
year = {2006},
}

TY - JOUR
AU - Fernando León-Saavedra
AU - Vladimír Müller
TI - Hypercyclic sequences of operators
JO - Studia Mathematica
PY - 2006
VL - 175
IS - 1
SP - 1
EP - 18
AB - 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.
LA - eng
KW - hypercyclic sequence; hypercyclic vector; hypercyclic subspace; essential minimum modulus
UR - http://eudml.org/doc/285126
ER -