{"paper":{"title":"Banach-valued Holomorphic Functions on the Maximal Ideal Space of H^\\infty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexander Brudnyi","submitted_at":"2011-03-11T19:11:08Z","abstract_excerpt":"We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H^\\infty of bounded holomorphic functions on the unit disk D\\subset C with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H^\\infty, prove that the maximal ideal space of the algebra H_{\\rm comp}^\\infty (A) of holomorphic functions on $\\Di$ with relatively compact images in a commutative unital complex Banach algebra A is homeomorphic to the direct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2347","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"}