Li-Yorke Chaotic Weighted Composition Operators

TL;DR

This paper characterizes Li-Yorke chaos for weighted composition operators across various function spaces, providing new criteria and extending understanding of chaotic behavior in weighted shifts and composition operators.

Contribution

It offers complete characterizations of Li-Yorke chaos for weighted composition operators on multiple spaces, including new criteria for weighted shifts on K"othe sequence spaces.

Findings

Characterizations of Li-Yorke chaos on $C_0(X)$ and $L^p(rac{}{})$ spaces.

Simple criteria for Li-Yorke chaotic weighted shifts on $c_0$ and $$ spaces.

Extension of chaos characterization to weighted shifts on Fre9chet sequence spaces.

Abstract

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