Multivariable Wold-Type Decomposition and Analytic Models for a class of left-inverse commuting pairs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911286663577600 |
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| author | Bhattacharjee, Monojit Gupta, Rajeev Venugopal, Vidhya |
| author_facet | Bhattacharjee, Monojit Gupta, Rajeev Venugopal, Vidhya |
| contents | This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a complete analytic model: every left-inverse commuting analytic toral $2$-isometric pair is unitarily equivalent to the pair of multiplication operator by co-ordinate functions $(M_{z_1}, M_{z_2})$ acting on some $\mathcal{E}$-valued Dirichlet-type space $\mathcal D_{\mathcal E}(μ_1, μ_2)$ associated with two finite positive operator-valued Borel measures $μ_1$ and $μ_2$ on the unit circle. An explicit functional model is further derived for the non-analytic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariable Wold-Type Decomposition and Analytic Models for a class of left-inverse commuting pairs Bhattacharjee, Monojit Gupta, Rajeev Venugopal, Vidhya Functional Analysis 46E20, 47B32, 47B38 This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a complete analytic model: every left-inverse commuting analytic toral $2$-isometric pair is unitarily equivalent to the pair of multiplication operator by co-ordinate functions $(M_{z_1}, M_{z_2})$ acting on some $\mathcal{E}$-valued Dirichlet-type space $\mathcal D_{\mathcal E}(μ_1, μ_2)$ associated with two finite positive operator-valued Borel measures $μ_1$ and $μ_2$ on the unit circle. An explicit functional model is further derived for the non-analytic case. |
| title | Multivariable Wold-Type Decomposition and Analytic Models for a class of left-inverse commuting pairs |
| topic | Functional Analysis 46E20, 47B32, 47B38 |
| url | https://arxiv.org/abs/2511.20632 |