A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911827783319552 |
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| author | Saini, Dimple Trivedi, Harsh Veerabathiran, Shankar |
| author_facet | Saini, Dimple Trivedi, Harsh Veerabathiran, Shankar |
| contents | Using the Wold-von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over $\mathbb{N}_0^{k}.$ As an application, we study a complete characterization of invariant subspaces for a doubly commuting pure isometric representation of the product system. This provides us a complete set of isomorphic invariants. Finally, we classify a large class of commuting isometric representations of the product system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_16674 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}$ Saini, Dimple Trivedi, Harsh Veerabathiran, Shankar Operator Algebras 46L08, 47A15, 47A80, 47B38, 47L55 Using the Wold-von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over $\mathbb{N}_0^{k}.$ As an application, we study a complete characterization of invariant subspaces for a doubly commuting pure isometric representation of the product system. This provides us a complete set of isomorphic invariants. Finally, we classify a large class of commuting isometric representations of the product system. |
| title | A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}$ |
| topic | Operator Algebras 46L08, 47A15, 47A80, 47B38, 47L55 |
| url | https://arxiv.org/abs/2308.16674 |