Endomorphisms of On which preserve the canonical UHF-subalgebra

Roberto Conti, Mikael Rørdam, Wojciech Szymanski

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Abstrakt

Unital endomorphisms of the Cuntz algebra On which preserve the canonical UHF-subalgebra Fn are investigated. We give examples of such endomorphisms λ=λu for which the associated unitary element u in On (which satisfies λ(Sj)=uSj for all j) does not belong to Fn. One such example, in the case when n=2, arises from a construction of a unital endomorphism of O2 which preserves the canonical UHF-subalgebra and where the relative commutant of its image in O2 contains a copy of O2.
Udgivelsesdato: 1 August
OriginalsprogEngelsk
TidsskriftJournal of Functional Analysis
Vol/bind259
Udgave nummer3
Sider (fra-til)602-617
Antal sider16
ISSN0022-1236
StatusUdgivet - 1. aug. 2009

Bibliografisk note

Paper id:: doi:10.1016/j.jfa.2010.03.027

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