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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/2405.14694 |
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| _version_ | 1866910457956139008 |
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| author | Joshi, Saee A. Sholapurkar, Vinayak M. |
| author_facet | Joshi, Saee A. Sholapurkar, Vinayak M. |
| contents | The process of identifying a Dirichlet-type space $D(μ)$ for a positive, Borel measure $μ$, supported on the unit circle $\mathbb T,$ with a de Branges-Rovnyak space was initiated by Sarason. A characterization of the symbol for a de Branges-Rovnyak spaces for which the shift operator is a $2$-isometry, was provided in an article by Kellay and Zarrabi. In this paper, capitalizing on the Aleman's model for the cyclic, analytic, completely hyperexpansive operators, we provide a characterization of cyclic, analytic, completely hyperexpansive operator with finite rank defect operator in terms of the symbol for a de Branges-Rovnyak space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completely hyperexpansive operators with finite rank defect operator and de Branges-Rovnyak spaces Joshi, Saee A. Sholapurkar, Vinayak M. Functional Analysis The process of identifying a Dirichlet-type space $D(μ)$ for a positive, Borel measure $μ$, supported on the unit circle $\mathbb T,$ with a de Branges-Rovnyak space was initiated by Sarason. A characterization of the symbol for a de Branges-Rovnyak spaces for which the shift operator is a $2$-isometry, was provided in an article by Kellay and Zarrabi. In this paper, capitalizing on the Aleman's model for the cyclic, analytic, completely hyperexpansive operators, we provide a characterization of cyclic, analytic, completely hyperexpansive operator with finite rank defect operator in terms of the symbol for a de Branges-Rovnyak space. |
| title | Completely hyperexpansive operators with finite rank defect operator and de Branges-Rovnyak spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.14694 |