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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12330 |
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| _version_ | 1866911316737785856 |
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| author | Ji, Guoxing |
| author_facet | Ji, Guoxing |
| contents | Let $\mathfrak A$ be a subdiagonal algebra with diagonal $\mathfrak D$ in a $σ$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $Φ$. We mainly consider the interpolation problem in $\mathfrak A$ with the universal factorization property. We determine when a finitely generated left ideal in $\mathfrak A$ is trivial. By constructing a periodic flow on $\mathcal M$ according to a type 1 subdiagonal algebra, we show that type 1 subdiagonal algebras coincide with analytic operator algebras associated with periodic flows in von Neumann algebras. This enables us to present a form decomposition of a type 1 subdiagonal algebra. As an application, we deduce a noncommutative operator-theoretic variant of the Corona theorem for type 1 subdiagonal algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpolation problems in subdiagonal algebras Ji, Guoxing Operator Algebras Functional Analysis Let $\mathfrak A$ be a subdiagonal algebra with diagonal $\mathfrak D$ in a $σ$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $Φ$. We mainly consider the interpolation problem in $\mathfrak A$ with the universal factorization property. We determine when a finitely generated left ideal in $\mathfrak A$ is trivial. By constructing a periodic flow on $\mathcal M$ according to a type 1 subdiagonal algebra, we show that type 1 subdiagonal algebras coincide with analytic operator algebras associated with periodic flows in von Neumann algebras. This enables us to present a form decomposition of a type 1 subdiagonal algebra. As an application, we deduce a noncommutative operator-theoretic variant of the Corona theorem for type 1 subdiagonal algebras. |
| title | Interpolation problems in subdiagonal algebras |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2512.12330 |