Weighted composition operators that are chaotic in the sense of Li and Yorke

Abstract

We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on C0(X) spaces and on Lp(μ) spaces (1 ≤ p < ∞). As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted shifts on c0 and on ℓp (1 ≤ p < ∞) that complement previously known results. We also investigate the notion of Li-Yorke chaos for weighted shifts on Fr´echet sequence spaces. As applications, we obtain characterizations of the Li-Yorke chaotic weighted shifts on K¨othe sequence spaces depending only on the entries of the K¨othe matrix and the weights of the shift.