Li-Yorke chaotic weighted composition operators on Hardy and Bergman spaces over the unit disk
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912964221599744 |
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| author | Álvarez, Carlos F. Carmo, João R. Manzur, Juan |
| author_facet | Álvarez, Carlos F. Carmo, João R. Manzur, Juan |
| contents | We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,φ}$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,φ}$ is (densely) Li--Yorke chaotic if and only if it is not power-bounded, and (densely) mean Li--Yorke chaotic if and only if it is not absolutely Cesàro bounded. These results are applied to Hardy spaces $H^p(\mathbb{D})$, $1 \le p \le \infty$, and weighted Bergman spaces $A^p_β(\mathbb{D})$, $-1 < β< \infty$ and $1 < p < \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02442 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Li-Yorke chaotic weighted composition operators on Hardy and Bergman spaces over the unit disk Álvarez, Carlos F. Carmo, João R. Manzur, Juan Functional Analysis Dynamical Systems Primary 47A16, 47B33, Secondary 30H10, 30H20 We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,φ}$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,φ}$ is (densely) Li--Yorke chaotic if and only if it is not power-bounded, and (densely) mean Li--Yorke chaotic if and only if it is not absolutely Cesàro bounded. These results are applied to Hardy spaces $H^p(\mathbb{D})$, $1 \le p \le \infty$, and weighted Bergman spaces $A^p_β(\mathbb{D})$, $-1 < β< \infty$ and $1 < p < \infty$. |
| title | Li-Yorke chaotic weighted composition operators on Hardy and Bergman spaces over the unit disk |
| topic | Functional Analysis Dynamical Systems Primary 47A16, 47B33, Secondary 30H10, 30H20 |
| url | https://arxiv.org/abs/2603.02442 |