文摘
It was shown recently by Conti, Rørdam and Szymański that there exist endomorphisms λu of the Cuntz algebra On such that λu(Fn)⊆Fn but u∉Fn, and a question was raised if for such a u there must always exist a unitary c80b8ec0f" title="Click to view the MathML source">v∈Fn with 33c4962aba98ffbadf6381fa6d" title="Click to view the MathML source">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)′∩Fn is finite dimensional.