$k$-Regular Factorizations and Joint Invariant Subspaces of Completely Non-Coisometric Row Contractions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911725397213184 |
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| author | Haria, Kalpesh J. Maurya, Aashish Kumar |
| author_facet | Haria, Kalpesh J. Maurya, Aashish Kumar |
| contents | This article investigates $k$-regular factorizations of characteristic functions associated with completely non-coisometric row contractions. In this setting, a one-to-one correspondence is established between chains of joint invariant subspaces
\[
\mathcal{M}_1 \subseteq \cdots \subseteq \mathcal{M}_{k-1}
\] and $k$-regular factorizations of the characteristic function of a completely non-coisometric row contraction. A functional model corresponding to a given $k$-regular factorization of a purely contractive multi-analytic operator satisfying the Szegő condition is further constructed, and the associated chain of joint invariant subspaces is characterized in terms of the underlying multi-analytic factors. Finally, it is shown that any such chain of joint invariant subspaces induces a block upper-triangular decomposition of the underlying row contraction, and that the characteristic function of each diagonal block coincides with the purely contractive part of the corresponding factor in the $k$-regular factorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $k$-Regular Factorizations and Joint Invariant Subspaces of Completely Non-Coisometric Row Contractions Haria, Kalpesh J. Maurya, Aashish Kumar Functional Analysis Operator Algebras 47A13, 47A15, 47A45, 47A68 (Primary) 47A20, 47A56 (Secondary) This article investigates $k$-regular factorizations of characteristic functions associated with completely non-coisometric row contractions. In this setting, a one-to-one correspondence is established between chains of joint invariant subspaces \[ \mathcal{M}_1 \subseteq \cdots \subseteq \mathcal{M}_{k-1} \] and $k$-regular factorizations of the characteristic function of a completely non-coisometric row contraction. A functional model corresponding to a given $k$-regular factorization of a purely contractive multi-analytic operator satisfying the Szegő condition is further constructed, and the associated chain of joint invariant subspaces is characterized in terms of the underlying multi-analytic factors. Finally, it is shown that any such chain of joint invariant subspaces induces a block upper-triangular decomposition of the underlying row contraction, and that the characteristic function of each diagonal block coincides with the purely contractive part of the corresponding factor in the $k$-regular factorization. |
| title | $k$-Regular Factorizations and Joint Invariant Subspaces of Completely Non-Coisometric Row Contractions |
| topic | Functional Analysis Operator Algebras 47A13, 47A15, 47A45, 47A68 (Primary) 47A20, 47A56 (Secondary) |
| url | https://arxiv.org/abs/2605.28895 |