On the Dynamics of Weighted Composition Operators II

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of continuous function spaces, such as the Banach spaces C₀(X) C 0 ( X ) of continuous scalar-valued functions vanishing at infinity on a Hausdorff locally compact space X , endowed with the sup norm, and the locally convex spaces C(X)c C ( X ) c of continuous scalar-valued functions on a completely regular space X , endowed with the compact-open topology. We also obtain complete characterizations of various notions of expansivity for weighted composition operators on Lᵖ(μ ) L p ( μ ) spaces, thereby complementing and extending previously known results in the unweighted case. Finally, we establish a conjugation between weighted and unweighted composition operators in the case of dissipative systems on Lᵖ(μ ) L p ( μ ) spaces and apply it to the study of several dynamical properties.