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On Endomorphisms of the Cuntz Algebra which Preserve the Canonical UHF-Subalgebra, II

2016/03/30 by Tomohiro Hayashi, Hayashi, Tomohiro, Jeong Hee Hong +3
Mathematics · #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1603.09044

openalex publication_date 2016/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It was shown recently by Conti, Rørdam and Szymański that there exist endomorphisms λu of the Cuntz algebra On such that λu (Fn)\subseteqFn but u\not\inFn, and a question was raised if for such a u there must always exist a unitary v\inFn with λu|Fn = λv|Fn. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms λu for which the relative commutant λu(Fn)'\capFn is finite dimensional.

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