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...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.展开更多
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
文摘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.
