{"paper":{"title":"Projective Freeness of Algebras of Bounded Holomorphic Functions on Infinitely Connected Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"A. Brudnyi","submitted_at":"2019-05-04T17:59:03Z","abstract_excerpt":"The algebra $H^\\infty(D)$ of bounded holomorphic functions on $D\\subset\\mathbb C$ is projective free for a wide class of infinitely connected domains. In particular, for such $D$ every rectangular left-invertible matrix with entries in $H^\\infty(D)$ can be extended in this class of matrices to an invertible square matrix (the generalization of the corona theorem for $H^\\infty(D)$). This follows from a new result on the structure of the maximal ideal space of $H^\\infty(D)$ asserting that its covering dimension is $2$ and the second \\v{C}ech cohomology group is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01532","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"}