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Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.
Ad un'algebra di von Neumann separabile , in forma standard su di uno spazio di Hilbert , si associa la algebra definita come la algebra costituita dai punti fissi dell'algebra di Cuntz generalizzata mediante l'azione canonica del gruppo degli unitari di . Si dà una caratterizzazione di nel caso in cui è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se è uno stato vettoriale normale e fedele di , la restrizione...
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