Cornel Pasnicu:Real rank zero and continuous fields of $C^*$-algebras, p.319-325

Abstract:

We give a necessary and sufficient condition for the $C^*$-algebra associated to an arbitrary continuous field of $C^*$-algebras to have real rank zero. Some applications of this result are given, including a characterization of the real rank zero property for the $C^*$-algebras with Hausdorff primitive spectrum.

Key Words: $C^*$-algebra, real rank zero, continuous field of $C^*$-algebras, the $C^*$-algebra associated to a continuous field of $C^*$-algebras, minimal tensor product of $C^*$-algebras, primitive spectrum.

2000 Mathematics Subject Classification: Primary: 46L05, ,
Secondary: 46L99, 46L85.

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