مشخصات پژوهش

In this paper, we study the hypercyclicity of the weighted translation $C_{u,g}$ defined on Orlicz space $L^{\Phi}(G)$ where $G$ is a locally compact group, $g\in G$ and $u$ is a weight function on $G$. It is shown that when $g\in G$ is a torsion element, then $C_{u,g}$ cannot be hypercyclic. However, for an aperiodic element $g\in G$, necessary and sufficient conditions for $C_{u,g}$ and its adjoint are given to be hypercyclic.