Purely infinite C*-algebras of real rank zero

被引:48
作者
Pasnicu, Cornel [1 ]
Rordam, Mikael [2 ]
机构
[1] Univ Puerto Rico, Dept Math, Rio Piedras, PR 00931 USA
[2] Univ So Denmark, Dept Math, DK-5230 Odense, Denmark
来源
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2007年 / 613卷
基金
美国国家科学基金会;
关键词
D O I
10.1515/CRELLE.2007.091
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 subset of I in the C*-algebra. It follows in particular that if A is any separable C*-algebra, then A circle times 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 circle times O-2 has the ideal property, also known as property (IP).
引用
收藏
页码:51 / 73
页数:23
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