{"paper":{"title":"Operator algebras for analytic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Christopher Ramsey, Kenneth R. Davidson, Orr Shalit","submitted_at":"2012-01-19T14:53:22Z","abstract_excerpt":"We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictions $\\mathcal M_V$ of the multiplier algebra $\\mathcal M$ of Drury-Arveson space to a holomorphic subvariety $V$ of the unit ball $\\mathbb{B}_d$.\n  We find that $\\mathcal M_V$ is completely isometrically isomorphic to $\\mathcal M_W$ if and only if $W$ is the image of $V$ under a biholomorphic automorphism of the ball. In this case, the isomorphism is unitarily implemented. This is then strengthend to show that, when $d<\\infty$, every isometric isomorphism is compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4072","kind":"arxiv","version":5},"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"}