On the Equi-nuclearity of Roe Algebras of Metric Spaces  

作　　者：Xiaoman CHEN Benyin FU Qin WANG 

机构地区：[1]School of Mathematical Sciences, Fudan University, Shanghai 200433, China [2]Department of Applied Mathematics, Donghua University, Shanghai 200051, China

出　　处：《Chinese Annals of Mathematics,Series B》2010年第4期519-528,共10页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.10731020,10971023);the Shu Guang Project of Shanghai Municipal Education Commission and Shanghai Education DepartmentFoundation(No.07SG38);the Foundation of the Ministry of Education of China

摘　　要：The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C＊（X） is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^＊ （X） is not nuclear.

关 键 词：Nuclear C^＊-algebra Uniform Roe algebra Equi-nuclear uniform Roe algebra 

分 类 号：O189.11[理学—数学] G633.62[理学—基础数学]