{"paper":{"title":"On Endomorphisms of the Cuntz Algebra which Preserve the Canonical UHF-Subalgebra, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jeong Hee Hong, Tomohiro Hayashi, Wojciech Szymanski","submitted_at":"2016-03-30T05:35:24Z","abstract_excerpt":"It was shown recently by Conti, R{\\o}rdam and Szyma\\'{n}ski that there exist endomorphisms $\\lambda_u$ of the Cuntz algebra $\\mathcal{O}_n$ such that $\\lambda_u (\\mathcal{F}_n)\\subseteq\\mathcal{F}_n$ but $u\\not\\in\\mathcal{F}_n$, and a question was raised if for such a $u$ there must always exist a unitary $v\\in\\mathcal{F}_n$ with $\\lambda_u|_{\\mathcal{F}_n} = \\lambda_v|_{\\mathcal{F}_n}$. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms $\\lambda_u$ for which the relative commutant $\\lambda_u(\\mathcal{F}_n)'\\cap\\mathcal{F}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09044","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"}