Hypercyclicity of Toeplitz operators with smooth symbols
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908765812424704 |
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| author | Fricain, Emmanuel Grivaux, Sophie Ostermann, Maëva |
| author_facet | Fricain, Emmanuel Grivaux, Sophie Ostermann, Maëva |
| contents | This paper is devoted to the study of the dynamics of Toeplitz operators $T_F$ with smooth symbols $F$ on the Hardy spaces of the unit disk $H^p$, $p>1$. Building on a model theory for Toeplitz operators on $H^2$ developed by Yakubovich in the 90's, we carry out an in-depth study of hypercyclicity properties of such operators. Under some rather general smoothness assumptions on the symbol, we provide some necessary/sufficient/necessary and sufficient conditions for $T_F$ to be hypercyclic on $H^p$. In particular, we extend previous results on the subject by Baranov-Lishanskii and Abakumov-Baranov-Charpentier-Lishanskii. We also study some other dynamical properties for this class of operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypercyclicity of Toeplitz operators with smooth symbols Fricain, Emmanuel Grivaux, Sophie Ostermann, Maëva Functional Analysis Complex Variables This paper is devoted to the study of the dynamics of Toeplitz operators $T_F$ with smooth symbols $F$ on the Hardy spaces of the unit disk $H^p$, $p>1$. Building on a model theory for Toeplitz operators on $H^2$ developed by Yakubovich in the 90's, we carry out an in-depth study of hypercyclicity properties of such operators. Under some rather general smoothness assumptions on the symbol, we provide some necessary/sufficient/necessary and sufficient conditions for $T_F$ to be hypercyclic on $H^p$. In particular, we extend previous results on the subject by Baranov-Lishanskii and Abakumov-Baranov-Charpentier-Lishanskii. We also study some other dynamical properties for this class of operators. |
| title | Hypercyclicity of Toeplitz operators with smooth symbols |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2502.03303 |