A new functional model for contractions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912280391712768 |
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| author | Yicao, Wang |
| author_facet | Yicao, Wang |
| contents | The paper presents a new functional model for completely non-unitary contractions on a Hilbert space. This model is based on the observation that the theory of contractions shares a common geometric basis with the extension theory of symmetric operators recently developed by the author in \cite{wang2024complex}. Compared with the now classical Sz.-Nagy-Foias model and the de Branges-Rovnyak model, ours is intrinsic in the sense that we need not construct a bigger space $H$ including the model space $\mathfrak{H}$ and realize the model operator on $\mathfrak{H}$ as the compression of a minimal unitary dilation on $H$. Our model space $\mathfrak{H}$ is constructed in a canonical and conceptually more direct manner and doesn't depend on the Sz. Nagy-Foias characteristic function explicitly. We also show how a contraction can be constructed from a marked Nevanlinna disc, which is the geometric analogue of the characteristic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new functional model for contractions Yicao, Wang Functional Analysis 47A20, 47A45, 47A67 The paper presents a new functional model for completely non-unitary contractions on a Hilbert space. This model is based on the observation that the theory of contractions shares a common geometric basis with the extension theory of symmetric operators recently developed by the author in \cite{wang2024complex}. Compared with the now classical Sz.-Nagy-Foias model and the de Branges-Rovnyak model, ours is intrinsic in the sense that we need not construct a bigger space $H$ including the model space $\mathfrak{H}$ and realize the model operator on $\mathfrak{H}$ as the compression of a minimal unitary dilation on $H$. Our model space $\mathfrak{H}$ is constructed in a canonical and conceptually more direct manner and doesn't depend on the Sz. Nagy-Foias characteristic function explicitly. We also show how a contraction can be constructed from a marked Nevanlinna disc, which is the geometric analogue of the characteristic function. |
| title | A new functional model for contractions |
| topic | Functional Analysis 47A20, 47A45, 47A67 |
| url | https://arxiv.org/abs/2503.13977 |