Purely infinite C*-algebras of real rank zero
Operator Algebras
2010-11-24 v3
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 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).
Keywords
Cite
@article{arxiv.math/0606378,
title = {Purely infinite C*-algebras of real rank zero},
author = {Cornel Pasnicu and Mikael Rordam},
journal= {arXiv preprint arXiv:math/0606378},
year = {2010}
}
Comments
24 pages. Revised version. Two earlier versions were mixtures of old and new versions, and even worse, the bibliography was missing in version 2!