{"paper":{"title":"Simplicity of UHF and Cuntz algebras on $L^p$~spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"N. Christopher Phillips","submitted_at":"2013-08-31T13:47:26Z","abstract_excerpt":"We prove that, for $p \\in [1, \\infty),$ and integers $d$ at least 2, the $L^p$ analog ${\\mathcal{O}}_d^p$ of the Cuntz algebra ${\\mathcal{O}}_d$ is a purely infinite simple amenable Banach algebra.\n  The proof requires what we call the spatial $L^p$ UHF algebras, which are analogs of UHF algebras acting on $L^p$ spaces. As for the usual UHF C*-algebras, they have associated supernatural numbers. For fixed $p \\in [1, \\infty),$ we prove that any spatial $L^p$ UHF algebra is simple and amenable, and that two such algebras are isomorphic if and only if they have the same supernatural number (equiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0115","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"}