Doubly commuting invariant subspaces for representations of product systems of $C^{\ast }$-correspondences

Abstract

We obtain a Shimorin-Wold-type decomposition for a doubly commuting covariant representation of a product system of $C^{\ast }$-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.

26pages, revised version

References in corpus (2)

• On C*-algebras generated by pairs of q-commuting isometries
• Generating wandering subspaces for doubly commuting covariant representations

Cited by in corpus (2)

• Beurling quotient subspaces for covariant representations of product systems
• Berger-Coburn-Lebow representation for pure isometric representations of product system over ${\mathbb{N}}_0^2$