On the Dynamics of Weighted Composition Operators

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