On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II

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Abstract

It was shown recently by Conti, Rørdam and Szymanskithat there exist exndomorphisms λ_uof the Cuntz algebra O_n such that λ_u(F_n) is contained in F_n but u does not belong to F_n, and a question was raised if for such a u there must always exist a unitary v in F_n with λ_u|_F_n = λ_v|_F_n. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms λ_u for which the relative commutant of λ_u(F_n) in F_n is finite dimensional.
Original languageEnglish
JournalJournal of Functional Analysis
Volume272
Issue number2
Pages (from-to)759-775
ISSN0022-1236
DOIs
Publication statusPublished - 2017

Keywords

  • Cuntz algebra
  • endomorphism
  • UHF-subalgebra

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