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 …

A Banach space operator T is said to be hypercyclic if there exists a vector x such that the
orbit {Tnx} is dense in the space. The most used tool to discover hypercyclic operators is …

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 …

We generalize the notions of hypercyclic operators, U U-frequently hypercyclic operators
and frequently hypercyclic operators by introducing a new concept in linear dynamics …

487 SOME RESULTS ON HYPERCYCLICITY OF TUPLE OF OPERATORS Abdelaziz
Tajmouati Mohammed El berrag 1. Introduction For a infinite-d Page 1 italian journal of pure …

The present article answers in the negative the great and long-standing problem in
hypercyclicity posed by D. Herrero: Is T⊕ T hypercyclic whenever T is? It also answers …

We provide in this paper a direct and constructive proof of the following fact: for a Banach
space $ X $ there are bounded linear operators having hypercyclic vectors if and only if $ X …

Recently a lot of research has been done on hypercyclicity of a bounded linear operator on
a Banach space, based on the hypercyclicity criterion obtained by Kitai in 1982, and …

The present article gives a brief discussion about operators which are weakly hypercyclic
and answers the following three questions:(i) Must T⊕ T be weakly hypercyclic whenever T …

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 …