A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}$
| Autor: | Saini, Dimple, Trivedi, Harsh, Veerabathiran, Shankar |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Complex Anal. Oper. Theory 18, 75 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11785-024-01520-6 |
| Popis: | 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. Comment: 20 pages |
| Databáze: | arXiv |
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