On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913496979996672 |
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| author | Chen, Cui Li, Yucheng Wang, Ya |
| author_facet | Chen, Cui Li, Yucheng Wang, Ya |
| contents | In this paper, we proved that $T_{z^n}$ acting on the $\mathbb{C}^m$-valued Hardy space $H_{\mathbb{C}^m}^2(\mathbb{D})$, is unitarily equivalent to $\bigoplus_1^{mn}T_z$, where $T_z$ is acting on the scalar-valued Hardy space $H_{\mathbb{C}}^2(\mathbb{D})$. And using the matrix manipulations combined with operator theory methods, we completely describe the reducing subspaces of $T_{z^n}$ on $H_{\mathbb{C}^m}^2(\mathbb{D})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space Chen, Cui Li, Yucheng Wang, Ya Functional Analysis In this paper, we proved that $T_{z^n}$ acting on the $\mathbb{C}^m$-valued Hardy space $H_{\mathbb{C}^m}^2(\mathbb{D})$, is unitarily equivalent to $\bigoplus_1^{mn}T_z$, where $T_z$ is acting on the scalar-valued Hardy space $H_{\mathbb{C}}^2(\mathbb{D})$. And using the matrix manipulations combined with operator theory methods, we completely describe the reducing subspaces of $T_{z^n}$ on $H_{\mathbb{C}^m}^2(\mathbb{D})$. |
| title | On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.07112 |