A double commutant theorem for purely large $C^*$-subalgebras of real rank zero corona algebras

Volume 190 / 2009

P. W. Ng Studia Mathematica 190 (2009), 135-145 MSC: Primary 46L35. DOI: 10.4064/sm190-2-3


Let ${\cal A}$ be a unital separable simple nuclear $C^*$-algebra such that ${{\cal M}({\cal A} \otimes {\cal K})}$ has real rank zero. Suppose that $\mathbb C$ is a separable simple liftable and purely large unital $C^*$-subalgebra of ${\cal M}({\cal A} \otimes {\cal K})/ ({\cal A} \otimes {\cal K})$. Then the relative double commutant of $\mathbb C$ in ${{\cal M}({\cal A}\otimes {\cal K})/({\cal A} \otimes {\cal K})}$ is equal to $\mathbb C$.


  • P. W. NgDepartment of Mathematics
    University of Louisiana
    217 Maxim D. Doucet Hall
    P.O. Box 41010
    Lafayette, LA 70504-1010, U.S.A.

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