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arXiv · 1903.07867

Doubly commuting invariant subspaces for representations of product systems of $C^*$-correspondences

Harsh Trivedi·Shankar Veerabathiran
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Abstract

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.

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Harsh Trivedi, Shankar Veerabathiran. 2019-03-19. Doubly commuting invariant subspaces for representations of product systems of $C^*$-correspondences. https://doi.org/10.1007/s43034-021-00136-7

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