Irreducible Representations of Inner Quasidiagonal $C^*$-Algebras

Canadian mathematical bulletin

Bruce Blackadar¹  Eberhard Kirchberg² 

[1] Department of Mathematics, University of Nevada, Reno, Reno, NV, U.S.A.;Institut für Mathematik, Humboldt Universität zu Berlin, Berlin, Germany

关键词: orderings of higher level;    division rings;    valuations;   

DOI  :  10.4153/CMB-2011-082-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

It is shown that a separable $C^*$-algebra is inner quasidiagonal if andonly if it has a separating family of quasidiagonal irreduciblerepresentations. As a consequence, a separable $C^*$-algebra is a strongNF algebra if and only if it is nuclear and has a separating family ofquasidiagonal irreducible representations. We also obtain some permanence properties of the class of innerquasidiagonal $C^*$-algebras.

【 授权许可】

Unknown