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...

We prove the existence of a non-trivial hyperinvariant subspace for several sets polynomially compact operators. The main results paper are: (i) norm closed algebra $$\mathcal {A}\subseteq \mathcal {B}(\mathscr {X})$$ which consists quasinilpotent operators has subspace; (ii) if there exists non-zero operator in closure generated by an band {S}$$ , then subspace.