文献类型：期刊文献

英文题名：REDUCED FREE PRODUCTS OF UNITAL AH ALGEBRAS AND BLACKADAR AND KIRCHBERG'S MF ALGEBRAS

作者：Hadwin, Don[1];Li, Jiankui[2];Shen, Junhao[1];Wang, Liguang[3]

机构：[1]Univ New Hampshire, Dept Math & Stat, Durham, NH 03824 USA;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[3]Qufu Normal Univ, Dept Math, Qufu, Shangdong, Peoples R China

年份：2012

卷号：68

期号：1

起止页码：275

外文期刊名：JOURNAL OF OPERATOR THEORY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000309484800015)】；

基金：Jiankui Li is partially supported by an NSF of China. Junhao Shen is partially supported by an NSF grant of U.S.A. Liguang Wang is partially supported by an NSF of China and the Department of Education of Shandong Province of China.

语种：英文

外文关键词：MF algebras; reduced free products; BDF semigroups

摘要：In the paper, we prove that reduced free products of unital AH algebras with respect to given faithful tracial states, in the sense of Voiculescu, are Blackadar and Kirhcberg's MF algebras. We also show that reduced free products of unital AM algebras with respect to given faithful tracial states, under mild conditions, are not quasidiagonal. Therefore we conclude, for a large class of AH algebras, that the Brown-Douglas-Fillmore extension semigroups of the reduced free products of these AH algebras with respect to given faithful tracial states are not groups. Our result is based on Haagerup and Thorbjornsen's work on the reduced C*-algebras of free groups.