Li-Yorke Chaotic Weighted Composition Operators

Abstract

We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on $C_0(X)$ spaces and on $L^p(\hat{I}¼)$ spaces. As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted shifts on $c_0$ and on ${\ell }^p$ ($1\le p<\infty$) that complement previously known results. We also investigate the notion of Li-Yorke chaos for weighted shifts on Fréchet sequence spaces. As applications, we obtain characterizations of the Li-Yorke chaotic weighted shifts on Köthe sequence spaces depending only on the entries of the Köthe matrix and the weights of the shift.