{"paper":{"title":"An algebra whose subalgebras are characterized by density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Alessandro Vignati","submitted_at":"2014-02-05T18:14:08Z","abstract_excerpt":"We refine a construction of Choi, Farah and Ozawa to build a nonseparable amenable operator algebra $\\mathcal A\\subseteq\\ell_\\infty(M_2)$ whose nonseparable subalgebras, including $\\mathcal A$, are not isomorphic to a $C^*$-algebra. This is done using a Luzin gap and a uniformly bounded group representation.\n  Next, we study additional properties of $\\mathcal A$ and of its separable subalgebras, related to the Kadison Kastler metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1112","kind":"arxiv","version":3},"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"}