Doubly commuting invariant subspaces for representations of product systems of \(C^\)-correspondences
We obtain a Shimorin-Wold-type decomposition for a doubly commuting covariant representation of a product system of \(C^*\)-correspondences. This extends a recent Wold-type decomposition by Jeu and Pinto for a \(q\)-doubly commuting isometries. Application to the wandering subspaces of doubly commut...
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| creator | Trivedi, Harsh Shankar Veerabathiran |
| description | We obtain a Shimorin-Wold-type decomposition for a doubly commuting covariant representation of a product system of \(C^*\)-correspondences. This extends a recent Wold-type decomposition by Jeu and Pinto for a \(q\)-doubly commuting isometries. Application to the wandering subspaces of doubly commuting induced representations is explored, and a version of Mandrekar's Beurling type theorem is obtained to study doubly commuting invariant subspaces using Fock space approach due to Popescu. |
| doi_str_mv | 10.48550/arxiv.1903.07867 |
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| subjects | Commuting Decomposition Representations Subspaces |
| title | Doubly commuting invariant subspaces for representations of product systems of \(C^\)-correspondences |
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