Title

Properties of Beurling-Type Submodules via Agler Decompositions

Publication Date

2017

Journal

Journal of Functional Analysis

Volume

272

Issue

1

First Page

83

Last Page

111

Abstract

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.

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