{"paper":{"title":"Lebesgue and Hardy Spaces for Symmetric Norms II: A Vector-Valued Beurling Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Don Hadwin, Yanni Chen, Ye Zhang","submitted_at":"2014-08-05T21:13:19Z","abstract_excerpt":"Suppose $\\alpha$ is a rotationally symmetric norm on $L^{\\infty}\\left(\\mathbb{T}\\right) $ and $\\beta$ is a \"nice\" norm on $L^{\\infty}\\left(\\Omega,\\mu \\right) $ where $\\mu$ is a $\\sigma$-finite measure on $\\Omega$. We prove a version of Beurling's invariant subspace theorem for the space $L^{\\beta}\\left(\\mu,H^{\\alpha}\\right) .$ Our proof uses the recent version of Beurling's theorem on $H^{\\alpha}\\left(\\mathbb{T}\\right) $ proved by the first author and measurable cross-section techniques. Our result significantly extends a result of H. Rezaei, S. Talebzadeh, and D. Y. Shin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1117","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"}