A characterization of invariant subspaces for isometric representations of product system over \(\mathbb{N}_0^{k}\)

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 complet...

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Bibliographic Details
Published inarXiv.org
Main Authors Saini, Dimple, Trivedi, Harsh, Shankar Veerabathiran
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.04.2024
Subjects
Invariants
Representations
Subspaces
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2308.16674