Commutants of a certain class of Toeplitz operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916656019668992 |
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| author | Bouhali, Aissa Louhichi, Issam Yousef, Abdel Rahman |
| author_facet | Bouhali, Aissa Louhichi, Issam Yousef, Abdel Rahman |
| contents | A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute with it. In this paper, we provide a complete description of bounded Toeplitz operators $T_f$, where the symbol $f$ has a truncated polar decomposition, that commute with a Toeplitz operator whose symbol is the sum of a quasihomogeneous function and a bounded analytic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Commutants of a certain class of Toeplitz operators Bouhali, Aissa Louhichi, Issam Yousef, Abdel Rahman Functional Analysis Complex Variables Operator Algebras Primary 47B35, Secondary 47L80 A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute with it. In this paper, we provide a complete description of bounded Toeplitz operators $T_f$, where the symbol $f$ has a truncated polar decomposition, that commute with a Toeplitz operator whose symbol is the sum of a quasihomogeneous function and a bounded analytic function. |
| title | Commutants of a certain class of Toeplitz operators |
| topic | Functional Analysis Complex Variables Operator Algebras Primary 47B35, Secondary 47L80 |
| url | https://arxiv.org/abs/2503.14200 |