Characteristic function of a power partial isometry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908579449012224 |
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| author | Babbar, Kritika Maji, Amit |
| author_facet | Babbar, Kritika Maji, Amit |
| contents | The celebrated Sz.-Nagy-Foiaş model theory says that there is a bijection between the class of purely contractive analytic functions and the class of completely non-unitary (c.n.u.) contractions modulo unitary equivalence. In this paper we provide a complete classification of the purely contractive analytic functions such that the associated contraction is a c.n.u. power partial isometry. As an application of our findings, we determine a class of contractive polynomials such that the associated c.n.u. power partial isometry is of the explicit diagonal form $S \oplus N \oplus C$, where $S$ and $C^*$ are unilateral shifts and $N$ is nilpotent. Finally, we obtain a characterization of operator-valued symbols for which the corresponding Toeplitz operator on vector-valued Hardy space is a partial isometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic function of a power partial isometry Babbar, Kritika Maji, Amit Functional Analysis Complex Variables Operator Algebras 47A45, 47A48, 47B35, 46E40, 47A20, 46E40, 30H10 The celebrated Sz.-Nagy-Foiaş model theory says that there is a bijection between the class of purely contractive analytic functions and the class of completely non-unitary (c.n.u.) contractions modulo unitary equivalence. In this paper we provide a complete classification of the purely contractive analytic functions such that the associated contraction is a c.n.u. power partial isometry. As an application of our findings, we determine a class of contractive polynomials such that the associated c.n.u. power partial isometry is of the explicit diagonal form $S \oplus N \oplus C$, where $S$ and $C^*$ are unilateral shifts and $N$ is nilpotent. Finally, we obtain a characterization of operator-valued symbols for which the corresponding Toeplitz operator on vector-valued Hardy space is a partial isometry. |
| title | Characteristic function of a power partial isometry |
| topic | Functional Analysis Complex Variables Operator Algebras 47A45, 47A48, 47B35, 46E40, 47A20, 46E40, 30H10 |
| url | https://arxiv.org/abs/2505.07824 |