1. Li-Yorke Chaotic Weighted Composition Operators
- Author
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Bernardes Jr., Nilson C. and Vasconcellos, Fernanda M.
- Subjects
Mathematics - Dynamical Systems ,Mathematics - Functional Analysis ,Primary 47A16, 47B33. Secondary 46E15, 46E30, 37B99 - 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.
- Published
- 2024