Li–Yorke chaotic weighted composition operators

We establish complete characterizations of the notion of Li–Yorke chaos for weighted composition operators on \(C_0(X)\) $C_0(X)$ spaces and on \(L^p(\mu )\) $L^p(\mu )$ spaces. As a consequence, we obtain simple characterizations of the Li–Yorke chaotic weighted shifts on \(c_0\) $c_0$ and on \(\ell ^p\) ${\ell }^p$ ( \(1 \le p < \infty \) $1\le p<\infty$ ) 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.