{"paper":{"title":"Topological Stable Rank of $H^\\infty(\\Omega)$ for Circular Domains $\\Omega$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Amol Sasane, Brett D. Wick, Raymond Mortini, Rudolf Rupp","submitted_at":"2009-09-14T12:28:41Z","abstract_excerpt":"Let $\\Omega$ be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by $H^\\infty(\\Omega)$ the Banach algebra of all bounded holomorphic functions on $\\Omega$, with pointwise operations and the supremum norm. We show that the topological stable rank of $H^\\infty(\\Omega)$ is equal to 2. The proof is based on Suarez's theorem that the topological stable rank of $H^\\infty(\\D)$ is equal to 2, where $\\D$ is the unit disk. We also show that for domains symmetric to the real axis, the Bass and topological stable ranks of the real symmetric algebra $H^\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2533","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"}