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 …

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 …

In this note, we show that every infinite-dimensional separable Fréchet space admitting a
continuous norm supports an operator for which there is an infinite-dimensional closed …

If X is a topological vector space and T: X→ X is a continuous linear mapping, then T is said
to be hypercyclic when there is a vector f in X such that the set {Tn f: n≥ 0} is dense in X …

Abstract Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the
locally convex direct sum of countably many copies of the Banach space ℓ1. We extend this …

Known results about hypercyclic subspaces concern either Fréchet spaces with a
continuous norm or the space ω. We fill the gap between these spaces by investigating …

Every infinite dimensional separable non-normable Fréchet space admits a continuous
hypercyclic operator. A large class of separable countable inductive limits of Banach spaces …

Let E be a separable Fréchet space. The operators T1,…, Tm are disjoint hypercyclic if there
exists x∈ E such that the orbit of (x,…, x) under (T1,…, Tm) is dense in E×⋯× E. We show …

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∈ …

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\} …