The Cowen-Douglas class and de Branges-Rovnyak spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912311169515520 |
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| author | Fricain, Emmanuel Sarkar, Jaydeb |
| author_facet | Fricain, Emmanuel Sarkar, Jaydeb |
| contents | We establish a connection between the de Branges-Rovnyak spaces and the Cowen-Douglas class of operators which is associated with complex geometric structures. We prove that the backward shift operator on a de Branges-Rovnyak space never belongs to the Cowen-Douglas class when the symbol is an extreme point of the closed unit ball of $H^\infty$ (the algebra of bounded analytic functions on the open unit disk). On the contrary, in the non extreme case, it always belongs to the Cowen-Douglas class of rank one. Additionally, we compute the curvature in this case and derive certain exotic results on unitary equivalence and angular derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Cowen-Douglas class and de Branges-Rovnyak spaces Fricain, Emmanuel Sarkar, Jaydeb Functional Analysis Complex Variables 47B13, 47A53, 46E22, 30H45, 32M15 We establish a connection between the de Branges-Rovnyak spaces and the Cowen-Douglas class of operators which is associated with complex geometric structures. We prove that the backward shift operator on a de Branges-Rovnyak space never belongs to the Cowen-Douglas class when the symbol is an extreme point of the closed unit ball of $H^\infty$ (the algebra of bounded analytic functions on the open unit disk). On the contrary, in the non extreme case, it always belongs to the Cowen-Douglas class of rank one. Additionally, we compute the curvature in this case and derive certain exotic results on unitary equivalence and angular derivatives. |
| title | The Cowen-Douglas class and de Branges-Rovnyak spaces |
| topic | Functional Analysis Complex Variables 47B13, 47A53, 46E22, 30H45, 32M15 |
| url | https://arxiv.org/abs/2504.04068 |