Certain classes of <italic>C</italic><sup>*</sup>-algebras preserved by tracial approximation

doi:10.1007/s11464-012-0196-3

Front Math Chin

2012, Vol. 7

Issue (3) : 449-458 https://doi.org/10.1007/s11464-012-0196-3

RESEARCH ARTICLE

Certain classes of C^*-algebras preserved by tracial approximation

Qingzhai FAN¹(

), Xiaochun FANG²

1. Institute of Mathematics, Shanghai Maritime University, Shanghai 201306, China; 2. Institute of Mathematics, Tongji University, Shanghai 200092, China

Download: PDF(142 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We show that the following classes of C^*-algebras in the classes Ω are inherited by simple unital C^*-algebras in the classes TAΩ: (1) simple unital purely infinite C^?-algebras, (2) unital isometrically rich C^*-algebras, (3) unital Riesz interpolation C^*-algebras.

Keywords C^*-algebras isometrically rich C^*-algebras Riesz interpolation C^*-algebras

Corresponding Author(s): FAN Qingzhai,Email:qzfan@shmtu.edu.cn

Issue Date: 01 June 2012

Cite this article:

Qingzhai FAN,Xiaochun FANG. Certain classes of C^*-algebras preserved by tracial approximation[J]. Front Math Chin, 2012, 7(3): 449-458.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0196-3
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I3/449

1	Brown L G, Pedersen G K. Non-stable K-theory and extremally rich C^-algebras. arXiv preprint math, OA/0708.3078*
2	Brown L G, Pedersen G K. Ideal structure and C^-algebras of low rank. Math Scand* , 2007, 100: 5-33
3	Elliott G A. On the classification of the inductive limits of sequences of semisimple finite dimensional algebras. J Algebra , 1976, 38: 29-44 doi: 10.1016/0021-8693(76)90242-8
4	Elliott G A, Niu Z. On tracial approximation. J Funct Anal , 2008, 254: 396-440 doi: 10.1016/j.jfa.2007.08.005
5	Fan Qingzhai. Classification of certain simple C^?-algebras. J Ramanujan Math Soc , 2011, 26: 1-7
6	Fan Qingzhai. Some C^-algebras properties preserved by tracial approximation. Israel J Math (to appear)*
7	Fan Qingzhai, Fang Xiaochun. Non-simple tracial approximation. Houston J Math , 2011, 37: 1249-1263
8	Fang Xiaochun. The classification of certain non-simple C^-algebras of tracial rank zero. J Funct Anal* , 2009, 256: 3861-3891 doi: 10.1016/j.jfa.2009.03.005
9	Lin H. The tracial topological rank of C^-algebras. Proc London Math Soc* , 2001, 83: 199-234 doi: 10.1112/plms/83.1.199
10	Lin H. An Introduction to The Classification of Amenable C^*-algebras. London, Singapore: World Scientific Publisher, 2001 doi: 10.1142/9789812799883
11	Niu Z. A classification of certain tracially approximately subhomogeneous C^-algebras. , University of Toronto* , 2005
12	Zhang S. A property of purely infinite simple C^-algebras. Proc Amer Math Soc* , 1990, 109: 717-720

Viewed

Full text

Abstract

Cited

Shared

Discussed