Purely infinite C*-algebras of real rank zero

Details Purely infinite C*-algebras of real rank zero Purely infinite C*-algebras of real rank zero

2006-06-15

arxiv.org/abs/math/0606378v3

J. Reine Angew. Math. 613 (2007), 51-73

Mathematics

Operator Algebras

24 pages. Revised version. Two earlier versions were mixtures of old and new versions, and even worse, the bibliography was mi

Scientific paper

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 K_0(I) -> K_0(I/J) is surjective for all closed two-sided ideals J contained in I in the C*-algebra. It follows in particular that if A is any separable C*-algebra, then A tensor O_2 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 tensor O_2 has the ideal property, also known as property (IP).

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