{"paper":{"title":"A Murray-von Neumann type classification of $C^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Chi-Keung Ng, Ngai-Ching Wong","submitted_at":"2011-12-07T01:39:42Z","abstract_excerpt":"We define type $\\mathfrak{A}$, type $\\mathfrak{B}$, type $\\mathfrak{C}$ as well as C*-semi-finite C*-algebras.\n  It is shown that a von Neumann algebra is a type $\\mathfrak{A}$, type $\\mathfrak{B}$, type $\\mathfrak{C}$ or C*-semi-finite C*-algebra if and only if it is, respectively, a type I, type II, type III or semi-finite von Neumann algebra. Any type I C*-algebra is of type $\\mathfrak{A}$ (actually, type $\\mathfrak{A}$ coincides with the discreteness as defined by Peligrad and Zsido), and any type II C*-algebra (as defined by Cuntz and Pedersen) is of type $\\mathfrak{B}$. Moreover, any typ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1455","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"}