Operator-valued rational functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866911665088364544 |
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| author | Curto, Raul E. Hwang, In Sung Lee, Woo Young |
| author_facet | Curto, Raul E. Hwang, In Sung Lee, Woo Young |
| contents | In this paper we show that every inner divisor of the operator-valued coordinate function, $zI_E$, is a Blaschke-Potapov factor. We also introduce a notion of operator-valued "rational" function and then show that $Δ$ is two-sided inner and rational if and only if it can be represented as a finite Blaschke-Potapov product; this extends to operator-valued functions the well-known result proved by V.P. Potapov for matrix-valued functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_11863 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Operator-valued rational functions Curto, Raul E. Hwang, In Sung Lee, Woo Young Functional Analysis 46E40, 30H10, 30J05, 47B35, 47B20 (Primary) In this paper we show that every inner divisor of the operator-valued coordinate function, $zI_E$, is a Blaschke-Potapov factor. We also introduce a notion of operator-valued "rational" function and then show that $Δ$ is two-sided inner and rational if and only if it can be represented as a finite Blaschke-Potapov product; this extends to operator-valued functions the well-known result proved by V.P. Potapov for matrix-valued functions. |
| title | Operator-valued rational functions |
| topic | Functional Analysis 46E40, 30H10, 30J05, 47B35, 47B20 (Primary) |
| url | https://arxiv.org/abs/2110.11863 |