华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (2): 5-12.

• 数学 统计学 • 上一篇    下一篇

具有迹实秩零的C*-代数(英)

姚洪亮1，2， 胡善文1   

  1. 1. 华东师范大学 数学系，上海 200062； 2. 河北大学 数学系，保定 071002
  • 收稿日期:2002-06-04 修回日期:2003-05-02 出版日期:2004-06-25 发布日期:2004-06-25
  • 通讯作者: 姚洪亮

C*-Algebras of Tracial Real Rank Zero

YAO Hong-liang1，2, HU Shan-wen1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China;2. Department of Mathematics, Hebei University, Baoding 071002, China
  • Received:2002-06-04 Revised:2003-05-02 Online:2004-06-25 Published:2004-06-25
  • Contact: YAO Hong-liang

摘要： 引入具有迹实秩零的C*-代数，并证明了具有迹实秩零的C*-代数与AF-代数的张量积仍是迹实秩零的，具有迹实秩零的单C*-代数是实秩零的.

关键词: C*-代数, 实秩, 迹实秩, C*-代数, 实秩, 迹实秩

Abstract: In this paper, we introduce a class of C*-algebras which have tracially real rank zero. We show that if A is a unital C*-algebra with tracial real rank zero and B is a AF-algebra, then A×B has tracial real rank zero. If a unital simple C*-algebra has tracially real rank zero, then it has real rank zero.

Key words: real rank, tracially real rank, C*-algebra, real rank, tracially real rank

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