{"paper":{"title":"Inner multipliers and Rudin type invariant subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Arup Chattopadhyay, B. Krishna Das, Jaydeb Sarkar","submitted_at":"2015-03-09T07:14:34Z","abstract_excerpt":"Let $\\mathcal{E}$ be a Hilbert space and $H^2_{\\mathcal{E}}(\\mathbb{D})$ be the $\\mathcal{E}$-valued Hardy space over the unit disc $\\mathbb{D}$ in $\\mathbb{C}$. The well known Beurling-Lax-Halmos theorem states that every shift invariant subspace of $H^2_{\\mathcal{E}}(\\mathbb{D})$ other than $\\{0\\}$ has the form $\\Theta H^2_{\\mathcal{E}_*}(\\mathbb{D})$, where $\\Theta$ is an operator-valued inner multiplier in $H^\\infty_{B(\\mathcal{E}_*, \\mathcal{E})}(\\mathbb{D})$ for some Hilbert space $\\mathcal{E}_*$. In this paper we identify $H^2(\\mathbb{D}^n)$ with $H^2(\\mathbb{D}^{n-1})$-valued Hardy spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02384","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"}