On stability of triangular factorization of positive operators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918149149949952 |
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| author | Belishev, M. I. Vakulenko, A. F. |
| author_facet | Belishev, M. I. Vakulenko, A. F. |
| contents | Let $\mathfrak f=\{\mathscr F_s\}_{s>0}$ be a nest and $C$ a bounded positive operator in a Hilbert space $\mathscr F$. The representation $C=V^*V$ provided $V\mathscr F_s\subset\mathscr F_s$ is a triangular factorization (TF) of $C$ w.r.t. $\mathfrak f$. The factorization is stable if $C^α\underset{α\to\infty}\to C$ and $C^α=V^{α\,*}V^α$ implies $V^α\to V$. If $C$ is positive definite (isomorphism), then TF is stable. The paper deals with the case of positive but not positive definite $C$. We impose some assumptions on $C^α$ and $C$ which provide the stability of TF. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On stability of triangular factorization of positive operators Belishev, M. I. Vakulenko, A. F. Functional Analysis Mathematical Physics 47Axx, 47B25, 35R30 Let $\mathfrak f=\{\mathscr F_s\}_{s>0}$ be a nest and $C$ a bounded positive operator in a Hilbert space $\mathscr F$. The representation $C=V^*V$ provided $V\mathscr F_s\subset\mathscr F_s$ is a triangular factorization (TF) of $C$ w.r.t. $\mathfrak f$. The factorization is stable if $C^α\underset{α\to\infty}\to C$ and $C^α=V^{α\,*}V^α$ implies $V^α\to V$. If $C$ is positive definite (isomorphism), then TF is stable. The paper deals with the case of positive but not positive definite $C$. We impose some assumptions on $C^α$ and $C$ which provide the stability of TF. |
| title | On stability of triangular factorization of positive operators |
| topic | Functional Analysis Mathematical Physics 47Axx, 47B25, 35R30 |
| url | https://arxiv.org/abs/2509.22765 |