Purely infinite C*-algebras of real rank zero

By C. Pasnicu, M. Rørdam. 2006

63 citations recorded by the source corpus.

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 K 0(I) → K 0(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).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d217f7f93bb307693ca0bc8abb085f2b8ba17fa7