{"paper":{"title":"Cross commutators of Rudin's submodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arup Chattopadhyay, B. Krishna Das, Jaydeb Sarkar","submitted_at":"2013-11-30T06:46:09Z","abstract_excerpt":"Let $b(z) = \\prod_{n=1}^\\infty \\frac{-\\bar{\\alpha}_n}{|\\alpha_n|} \\frac{z - \\alpha_n}{1 - \\bar{\\alpha}_n z}$, where $\\sum_{n=1}^\\infty (1 - |\\alpha_n|) <\\infty$, be the Blaschke product with zeros at $\\alpha_n \\in \\mathbb{D} \\setminus \\{0\\}$. Then $\\cls = \\vee_{n=1}^\\infty \\big(z^n H^2(\\mathbb{D})\\big) \\otimes \\big(\\prod_{k=n}^\\infty \\frac{-\\bar{\\alpha}_n}{|\\alpha_n|} \\frac{z - \\alpha_n}{1 - \\bar{\\alpha}_n z} H^2(\\mathbb{D})\\big)$ is a joint $(M_{z_1}, M_{z_2})$ invariant subspace of the Hardy space $H^2(\\mathbb{D}^2) \\cong H^2(\\mathbb{D}) \\otimes H^2(\\mathbb{D})$. This class of subspaces was "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0070","kind":"arxiv","version":2},"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"}