On the Dynamics of Weighted Composition Operators

Abstract

We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Cesà ro boundedness and mean Li-Yorke chaos for weighted composition operators on $L^p(\hat{I}¼)$ spaces and on $C_0(\hat{I}\text{c◯})$ spaces. We illustrate the general results by presenting several applications to weighted shifts on the classical sequence spaces $c_0(\mathbb{N})$, $c_0(\mathbb{Z})$, ${\ell }^p(\mathbb{N})$ and ${\ell }^p(\mathbb{Z})$ ($1\le p<\infty$) and to weighted translation operators on the classical function spaces $C_0[1,\infty )$, $C_0(\mathbb{R})$, $L^p[1,\infty )$ and $L^p(\mathbb{R})$ ($1\le p<\infty$).