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 …

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 …

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 …

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 bounded linear operator T on a Banach space X is called subspace-hypercyclic for a
subspace M if Orb (T, x)∩ M is dense in M for a vector x∈ M. We show examples that …

By a recent result of M. De La Rosa and C. Read, there exist hypercyclic Banach space
operators which do not satisfy the Hypercyclicity Criterion. In the present paper, we prove …

In this short note, we prove that for a dense set A⊂ X (X is a Banach space) there is a non-
trivial closed subspace M⊂ X such that A∩ M is dense in M. We use this result to answer a …

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\} …

In this paper we study an operator $ T $ on a Banach space $ E $ which is $ M $-hypercyclic
for some subspace $ M $ of $ E $. We give a sufficient condition for such an operator to be …