Which hyponormal block Toeplitz operators are either normal or analytic?
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909610632282112 |
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| author | Zhu, Senhua Lu, Yufeng Zu, Chao |
| author_facet | Zhu, Senhua Lu, Yufeng Zu, Chao |
| contents | In this paper, we continue Curto-Hwang-Lee's work to study the connection between hyponormality and subnormality for block Toeplitz operators acting on the vector-valued Hardy space of the unit circle. Curto-Hwang-Lee's work focuses primarily on hyponormality and subnormality of block Toeplitz operators with rational symbols. By studying the greatest common divisor of matrix-valued inner functions and the ``weak" commutativity of matrix-valued inner functions, we extended Curto-Hwang-Lee's result to block Toeplitz operators with symbols of bounded type. More precisely, we proved that if $Ψ,Ψ^{\ast}$ are matrix-valued functions of bounded type and the inner part of $Ψ$ of Douglas-Shapiro-Shields factorization is a scalar inner function, then every hyponormal Toeplitz operator $T_Ψ$ whose square is also hyponormal must be either normal or analytic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01373 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Which hyponormal block Toeplitz operators are either normal or analytic? Zhu, Senhua Lu, Yufeng Zu, Chao Functional Analysis Primary 47B35, 46E40, Secondary 47B20 In this paper, we continue Curto-Hwang-Lee's work to study the connection between hyponormality and subnormality for block Toeplitz operators acting on the vector-valued Hardy space of the unit circle. Curto-Hwang-Lee's work focuses primarily on hyponormality and subnormality of block Toeplitz operators with rational symbols. By studying the greatest common divisor of matrix-valued inner functions and the ``weak" commutativity of matrix-valued inner functions, we extended Curto-Hwang-Lee's result to block Toeplitz operators with symbols of bounded type. More precisely, we proved that if $Ψ,Ψ^{\ast}$ are matrix-valued functions of bounded type and the inner part of $Ψ$ of Douglas-Shapiro-Shields factorization is a scalar inner function, then every hyponormal Toeplitz operator $T_Ψ$ whose square is also hyponormal must be either normal or analytic. |
| title | Which hyponormal block Toeplitz operators are either normal or analytic? |
| topic | Functional Analysis Primary 47B35, 46E40, Secondary 47B20 |
| url | https://arxiv.org/abs/2308.01373 |