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∈ …

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

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 …

We treat the question of existence of common hypercyclic vectors for families of continuous
linear operators. It is shown that for any continuous linear operator T on a complex Fréchet …

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 …

On the Fréchet space of entire functions H (C), we show that every nonscalar continuous
linear operator L: H (C)→ H (C) which commutes with differentiation has a hypercyclic vector …

We study in this paper a hypercyclicity property of linear dynamical systems: a bounded
linear operator T acting on a separable infinite-dimensional Banach space X is said to be …

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 bounded linear operator $ T $ on a Banach space $ X $ is called frequently hypercyclic if
there exists $ x\in X $ such that the lower density of the set $\{n\in\mathbb {N}: T^ nx\in U\} …

We provide with criteria for a family of sequences of operators to share a frequently universal
vector. These criteria are inspired by the classical Frequent Hypercyclicity Criterion and by a …