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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06067 |
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| _version_ | 1866909411096657920 |
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| author | Chattopadhyay, Arup Jana, Supratim |
| author_facet | Chattopadhyay, Arup Jana, Supratim |
| contents | In the classical Hardy space $H^2(\mathbb{D})$, it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator $S^{*}$. It appears in this paper that kernels of finite rank perturbations of Hankel operators are almost shift invariant as well as nearly $S^*$- invariant with finite defect. This allows us to obtain a structure of the kernel in several important cases by applying a recent theorem due to Chalendar, Gallardo, and Partington. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kernels of Perturbed Hankel Operators Chattopadhyay, Arup Jana, Supratim Functional Analysis 47B35, 47B38 In the classical Hardy space $H^2(\mathbb{D})$, it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator $S^{*}$. It appears in this paper that kernels of finite rank perturbations of Hankel operators are almost shift invariant as well as nearly $S^*$- invariant with finite defect. This allows us to obtain a structure of the kernel in several important cases by applying a recent theorem due to Chalendar, Gallardo, and Partington. |
| title | Kernels of Perturbed Hankel Operators |
| topic | Functional Analysis 47B35, 47B38 |
| url | https://arxiv.org/abs/2404.06067 |