Abstract
If ω1, ω2 are two pure gauge-invariant states of the Cuntz algebra Od, we show that there is an automorphism α of Od such that ω1=ω2∘α. If ω is a general pure state on Od and ϕ0 is a given Cuntz state, we show that there exists an endomorphism α of Od such that ϕ0=ω∘α.
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