Endomorphisms of On which preserve the canonical UHF-subalgebra
Abstract
Unital endomorphisms of the Cuntz algebra On which preserve the canonical UHF-subalgebra Fn of On are investigated. We give examples of such endomorphisms for which the associated unitary element in On does not belong to Fn. One such example, in the case where n=2, arises from a construction of a unital endomorphism on O2 which preserves the canonical UHF-subalgebra and where the relative commutant of the image in O2 contains a copy of O2.
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