Properties of Beurling-Type Submodules via Agler Decompositions
Journal of Functional Analysis
In this paper, we study operator-theoretic properties of the compressed shift operators S_z1 and S_z2 on complements of submodules of the Hardy space over the bidisk H^2(D^2). Specifically, we study Beurling-type submodules using properties of Agler decompositions to deduce properties of S_z1 and S_z2 on model spaces. Results include characterizations of when a commutator has rank n and when subspaces associated to Agler decompositions are reducing for S_z1 and S_z2 . We include several open questions.
Bickel, Kelly and Liaw, Constanze. "Properties of Beurling-Type Submodules via Agler Decompositions." Journal of Functional Analysis (2017) : 83-111.