{"paper":{"title":"A Generalized Beurling Theorem in Finite von Neumann Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Don Hadwin, Lauren Sager, Wenjing Liu","submitted_at":"2018-07-26T01:50:55Z","abstract_excerpt":"In 2016 and 2017, Haihui Fan, Don Hadwin and Wenjing Liu proved a commutative and noncommutative version of Beurling's theorems for a continuous unitarily invariant norm $\\alpha $ on $L^{\\infty}(\\mathbb{T},\\mu)$ and tracial finite von Neumann algebras $\\left( \\mathcal{M},\\tau \\right) $, respectively. In the paper, we study unitarily $\\|\\|_{1}$-dominating invariant norms $\\alpha $ on finite von Neumann algebras. First we get a Burling theorem in commutative von Neumann algebras by defining $H^{\\alpha}(\\mathbb{T},\\mu)=\\overline {H^{\\infty}(\\mathbb{T},\\mu)}^{\\sigma(L^{\\alpha}\\left(\n  \\mathbb{T} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09916","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"}