{"paper":{"title":"Transitivity and bundle shifts","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anjian Xu, Ronald G. Douglas","submitted_at":"2014-03-20T03:34:46Z","abstract_excerpt":"A subalgebra $A$ of the algebra $B(\\mathcal{H})$ of bounded linear operators on a separable Hilbert space $\\mathcal{H}$ is said to be catalytic if every transitive subalgebra $\\mathcal{T}\\subset B(\\mathcal{H})$ containing it is strongly dense. We show that for a hypo-Dirichlet or logmodular algebra, $A=H^{\\infty}(m)$ acting on a generalized Hardy space $H^{2}(m)$ for a representing measure $m$ that defines a reproducing kernel Hilbert space is catalytic. For the case of a nice finitely-connected domain, we show that the \"holomorphic functions\" of a bundle shift yields a catalytic algebra, thus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5032","kind":"arxiv","version":2},"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"}