华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (3): 8-14.

• 数学 统计学 • 上一篇    下一篇

C*-代数迹极限性质的封闭性(英)

肖 翔1, 胡善文2   

  1. 1. 上海工程技术大学 基础学院, 上海 200336;2. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2004-06-14 修回日期:2004-12-17 出版日期:2006-05-25 发布日期:2006-05-25
  • 通讯作者: 肖 翔

Closing Property of C*-Algebras with Tracial Limit(English)

XIAO Xiang1, HU Shan-wen2   

  1. 1. Fundamental College, Shanghai University of Engineering Science, Shanghai 200336, China}; 2. Department of Mathematics, East China Normal University,Shanghai 200062, China
  • Received:2004-06-14 Revised:2004-12-17 Online:2006-05-25 Published:2006-05-25
  • Contact: XIAO Xiang

摘要： 在迹极限的意义下, 特别是在单代数的条件下, 研究某些C*-代数性质的封闭性.假设A=(t2)limn -> ∞ (An,pn), An上至少有一个迹态或An,具有(SP) 性质，则A也有相同的结果;假设A=(t3)limn -> ∞ (An,pn),并且A是单代数,如果\TR(An)=0,tsr(An)=1和An具有投影消去律,
则A也有相同的结果.

关键词: 迹极限, C*-代数, 封闭性, 迹极限, C*-代数, 封闭性

Abstract: It was shown that there are some C*-algebras maintaining the closing property with the tracial limit, especially under the condition of simplicity. Suppose A=(t2)limn -> ∞ (An,pn). If each An admits at least one tracial state or has SP-property, then A has the same case. Suppose A=(t3)limn -> ∞ (An,pn) and A is simple. If TR(An)=0, tsr(An)=1 and An has Cancelation of Projection, then A has the same case.

Key words: C*-algebras, closing property, tracial limit, C*-algebras, closing property

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