Generating wandering subspaces for doubly commuting covariant representations

Abstract

We obtain a Halmos-Richter-type wandering subspace theorem for covariant representations of C*-correspondences. Further the notion of Cauchy dual and a version of Shimorin's Wold-type decomposition for covariant representations of C*-correspondences is explored and as an application a wandering subspace theorem for doubly commuting covariant representations is derived. Using this wandering subspace theorem generating wandering subspaces are characterized for covariant representations of product systems in terms of the doubly commutativity condition.

21pages

References in corpus (1)

• Covariant representations of subproduct systems

Cited by in corpus (4)

• Regular covariant representations and their Wold-type decomposition
• Doubly commuting invariant subspaces for representations of product systems of $C^{\ast }$-correspondences
• Cauchy dual and Wold-type decomposition for bi-regular covariant representations
• A characterization of invariant subspaces for isometric representations of product system over ${\mathbb{N}}_0^k$