本系列报告将从基础讲起, 介绍一系列C*-代数的正则性质, 如稳定秩, 迹逼近与迹秩, 核性与核维数, 关于正元的比较定理, 江-苏代数稳定性等等. 其中重点报告的结果是AF-代数的分类定理, 江-苏代数的构造, 零阶映射的结构定理, 具有有限核维数将蕴含关于正元的严格比较定理等, 并介绍关于C*-代数迹逼近的一些最新进展. 

 

预备知识: 泛函分析

 

参考资料: 

1.  H. Lin, An introduction to the classification of amenable C∗-algebras, World Scientific Publishing Co. Inc. River Edge, NJ, 2001, xii+320 pp, ISBN: 981-02-4680-3.

2.  M. Rordam, On the structure of simple C∗-algebras tensored with a UHF-algebra. II, J. Funct. Anal. 107 (1992), 255-269. 

3.  X. Jiang and H. Su, On a simple unital projectionless C*-algebra, Amer. J. Math. 121(1999), no. 2, 359-413.

4.   W. Winter and J. Zacharias, Completely positive maps of order zero, Munster J. Math. 2 (2009), 311-324. 

5.  W. Winter and J. Zacharias, The nuclear dimension of C*-algebras, Adv. Math. 224 (2010), 461-498.

6.  Leonel Robert,  Nuclear dimension and n-comparison. Munster J. Math. 4 (2011), 65–71.  

 

 

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