{"paper":{"title":"Properties of Beurling-Type Submodules via Agler Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Constanze Liaw, Kelly Bickel","submitted_at":"2014-11-21T03:49:56Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5759","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}