LIMITS OF PURE FUNCTIONALS OF C*-ALGEBRAS

被引：0
|
作者：
Shah, M. H. [1 ]
机构：
[1] LUMS, Dept Math, Lahore 54792, Pakistan
来源：
JOURNAL OF OPERATOR THEORY | 2010年 / 63卷 / 02期
关键词：
Pure state; pure functional; irreducible representation; C*-algebra; spectrum; STATES; TRACE;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that, for a C*-algebra A, every (weak*-) limit of pure functionals is a multiple of a pure functional if and only if every limit of pure states is a multiple of pure states (a condition previously studied by Glimm). On the other hand, it is shown that the set of pure states P(A) being closed does not force the set of pure functionals <(G(A))over bar> to be closed. The conditions G(A) = G(A) and <(G(A))over bar> = G(A) U {0} are characterised in terms of sums of homogeneous C*-algebras.
引用
收藏
页码：349 / 362
页数：14
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