Abstract 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 () 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 () L p (μ) spaces and apply it to the study of several dynamical properties.
Bernardes et al. (Tue,) studied this question.