A continuous linear operator T on a Fréchet space F is hypercyclic if there exists a vector f∈
F (which is called hypercyclic for T) such that the orbit {T nf: n∈ N} is dense in F. A subset M …

We show that under no hypotheses on the density of the ranges of the mappings involved,
an almost-commuting sequence (Tn) of operators on an F-space X satisfies the …

Hypercyclicity is the study of linear and continuous operators that possess a dense orbit.
Given a separable, infinite dimensional topological vector space X, we say a continuous …

A continuous linear operator T: X→ X is hypercyclic if there is an x∈ X such that the orbit
{Tnx} is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that …

A continuous linear operator on a Fréchet space X is frequently hypercyclic if there exists a
vector x such that for any nonempty open subset U⊂ X the set of n∈ N∪{0} for which T nx∈ …

An operator T acting on a separable F-space X is called hypercyclic if there exists f∈ X such
that the orbit {T nf} is dense in X. Here we determine when an operator that λ-commutes with …

A bounded linear operator T on a Banach space X is called hypercyclic if there exists a
vector x∈ X such that its orbit,{T nx}, is dense in X. In this paper we show hypercyclic …

A continuous linear operator T: X→ X on a topological vector space X is called hypercyclic if
there is x∈ X such that the orbit [Formula: see text] is dense in X. We establish a criterion for …

We investigate the subject of linear dynamics by studying the notion of frequent
hypercyclicity for bounded operators $ T $ on separable complex $\mathcal {F} $-spaces …

In 1969 Rolewicz raised the question whether every separable infinite dimensional Banach
space admits a hypercyclic operator. This question was answered recently in the positive …