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Doubly commuting invariant subspaces for representations of product systems of $C^*$-correspondences (1903.07867v3)
Published 19 Mar 2019 in math.OA and math.FA
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.