{"paper":{"title":"The Toeplitz corona problem for algebras of multipliers on a Nevanlinna-Pick space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mrinal Raghupathi, Ryan Hamilton","submitted_at":"2011-04-19T18:03:16Z","abstract_excerpt":"Suppose $\\fA$ is an algebra of operators on a Hilbert space $H$ and $A_1,..., A_n \\in \\fA$. If the row operator $[A_1,..., A_n] \\in B(H^{(n)},H)$ has a right inverse in $B(H, H^{(n)})$, the Toeplitz corona problem for $\\fA$ asks if a right inverse can be found with entries in $\\fA$. When $H$ is a complete Nevanlinna-Pick space and $\\fA$ is a weakly-closed algebra of multiplication operators on $H$, we show that under a stronger hypothesis, the corona problem for $\\fA$ has a solution. When $\\fA$ is the full multiplier algebra of $H$, the Toeplitz corona theorems of Arveson, Schubert and Ball-Tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3821","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"}