Over time the concept of hypercyclicity has been explored in different manners and contexts, gaining new forms applications. In particular when space an adjacent structure, we can always look for sets hypercyclic vectors compatible with that framework. this paper deal operators acting on Fréchet sequence algebras give criteria existence common disjoint algebras.

In this paper, we study the so-called Bishop operators Tα on Lp([0,1]), with α∈(0,1) and 1<p<+∞, from point of view linear dynamics. We show that they are never hypercyclic nor supercyclic, investigate extensions these results to case weighted translation operators. then cyclicity Tα. Building by Chalendar Partington in where α is rational, cyclic for a dense Gδ-set irrational α's, discuss func...

This paper establishes decomposability for composition operators induced on the Hardy spaces H (1 ≤ p < ∞) by parabolic linear fractional self-maps of the unit disc that are not automorphisms. This result, along with a recent theorem of Miller and Miller [15], shows that no such composition operator is supercyclic. The work here completes part of a previous investigation [1] where the author an...

For a sequence {Tn} of continuous linear operators on a separable Fréchet space X, we discuss necessary conditions and sufficient conditions for {Tn} to be topologically mixing, and the relations between topological mixing and the Hypercyclicity Criterion. Among them are: 1) topological mixing is equivalent to being hereditarily densely hypercyclic; 2) the Hypercyclicity Criterion with respect ...