{"paper":{"title":"Free Products of Generalized RFD C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Don Hadwin","submitted_at":"2011-07-30T07:36:40Z","abstract_excerpt":"If $k$ is an infinite cardinal, we say a C*-algebra $\\mathcal{A}$ is residually less than $k$ dimensional, $R_{<k}D,$ if the family of representations of $\\mathcal{A}$ on Hilbert spaces of dimension less than $k$ separates the points of $\\mathcal{A}.$ We give characterizations of this property, and we show that if $\\{\\mathcal{A}_{i}:i\\in I\\} $ is a family of $R_{<k}D$ algebras, then the free product $\\underset{i\\in I}{\\ast}\\mathcal{A}_{i}$ is $R_{<k}D$. If each $\\mathcal{A}_{i}$ is unital, we give sufficient conditions, depending on the cardinal $k$, for the free product $\\underset{i\\in I}{\\as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0049","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"}