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Abstract
We show that a separable purely infinite C*-algebra is of real rank zero if and only if its primitive ideal space has a basis consisting of compact-open sets and the natural map K0(I) → K0(I/J) is surjective for all closed two-sided ideals J⊂I in the C*-algebra. It follows in particular that if A is any separable C*-algebra, then A ⊗𝒪2 is of real rank zero if and only if the primitive ideal space of A has a basis of compact-open sets, which again happens if and only if A ⊗ 𝒪2 has the ideal property, also known as property (IP).
Received: 2006-06-30
Published Online: 2008-02-05
Published in Print: 2007-12-19
© Walter de Gruyter
