Properties of Beurling-type submodules via Agler decompositions
| Autor: | Kelly Bickel, Constanze Liaw |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Mathematics::Operator Algebras Mathematics::Complex Variables Mathematics - Complex Variables 010102 general mathematics Commutator (electric) Hardy space Type (model theory) Rank (differential topology) 01 natural sciences Linear subspace law.invention Combinatorics symbols.namesake 47A13 47A20 46E22 law 0103 physical sciences FOS: Mathematics symbols 010307 mathematical physics Complex Variables (math.CV) 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 272:83-111 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2016.10.007 |
| Popis: | In this paper, we study operator-theoretic properties of the compressed shift operators $S_{z_1}$ and $S_{z_2}$ on complements of submodules of the Hardy space over the bidisk $H^2(\mathbb{D}^2)$. Specifically, we study Beurling-type submodules - namely submodules of the form $\theta H^2(\mathbb{D}^2)$ for $\theta$ inner - using properties of Agler decompositions of $\theta$ to deduce properties of $S_{z_1}$ and $S_{z_2}$ on model spaces $H^2(\mathbb{D}^2) \ominus \theta H^2(\mathbb{D}^2)$. Results include characterizations (in terms of $\theta$) of when a commutator $[S_{z_j}^*, S_{z_j}]$ has rank $n$ and when subspaces associated to Agler decompositions are reducing for $S_{z_1}$ and $S_{z_2}$. We include several open questions. Comment: 25 pages |
| Databáze: | OpenAIRE |
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