On the Dynamics of Weighted Composition Operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912752758423552 |
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| author | Bernardes Jr., Nilson C. Bonilla, Antonio Pinto, João V. A. |
| author_facet | Bernardes Jr., Nilson C. Bonilla, Antonio Pinto, João V. A. |
| contents | We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Cesàro boundedness and mean Li-Yorke chaos for weighted composition operators on $L^p(μ)$ spaces and on $C_0(Ω)$ spaces. We illustrate the general results by presenting several applications to weighted shifts on the classical sequence spaces $c_0(\mathbb{N})$, $c_0(\mathbb{Z})$, $\ell^p(\mathbb{N})$ and $\ell^p(\mathbb{Z})$ ($1 \leq p < \infty$) and to weighted translation operators on the classical function spaces $C_0[1,\infty)$, $C_0(\mathbb{R})$, $L^p[1,\infty)$ and $L^p(\mathbb{R})$ ($1 \leq p < \infty$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Dynamics of Weighted Composition Operators Bernardes Jr., Nilson C. Bonilla, Antonio Pinto, João V. A. Dynamical Systems Functional Analysis Primary 47A16, 47B33. Secondary 46E15, 46E30 We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Cesàro boundedness and mean Li-Yorke chaos for weighted composition operators on $L^p(μ)$ spaces and on $C_0(Ω)$ spaces. We illustrate the general results by presenting several applications to weighted shifts on the classical sequence spaces $c_0(\mathbb{N})$, $c_0(\mathbb{Z})$, $\ell^p(\mathbb{N})$ and $\ell^p(\mathbb{Z})$ ($1 \leq p < \infty$) and to weighted translation operators on the classical function spaces $C_0[1,\infty)$, $C_0(\mathbb{R})$, $L^p[1,\infty)$ and $L^p(\mathbb{R})$ ($1 \leq p < \infty$). |
| title | On the Dynamics of Weighted Composition Operators |
| topic | Dynamical Systems Functional Analysis Primary 47A16, 47B33. Secondary 46E15, 46E30 |
| url | https://arxiv.org/abs/2506.04476 |