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arXiv · 2407.19091

Li-Yorke Chaotic Weighted Composition Operators

Nilson C. Bernardes Jr.·Fernanda M. Vasconcellos
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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.

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Nilson C. Bernardes Jr., Fernanda M. Vasconcellos. 2024-07-26. Li-Yorke Chaotic Weighted Composition Operators. https://arxiv.org/abs/2407.19091

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