Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589518 | Journal of Functional Analysis | 2017 | 29 Pages |
Abstract
In this paper, we study operator-theoretic properties of the compressed shift operators Sz1Sz1 and Sz2Sz2 on complements of submodules of the Hardy space over the bidisk H2(D2)H2(D2). Specifically, we study Beurling-type submodules – namely submodules of the form θH2(D2)θH2(D2) for θ inner – using properties of Agler decompositions of θ to deduce properties of Sz1Sz1 and Sz2Sz2 on model spaces H2(D2)⊖θH2(D2)H2(D2)⊖θH2(D2). Results include characterizations (in terms of θ ) of when a commutator [Szj⁎,Szj] has rank n and when subspaces associated to Agler decompositions are reducing for Sz1Sz1 and Sz2Sz2. We include several open questions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kelly Bickel, Constanze Liaw,