On ultraproducts of operator algebras  

作　　者：LI Weihua 

机构地区：[1]Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100080, China

出　　处：《Science China Mathematics》2005年第9期1284-1295,共12页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10471137).

摘　　要：Some basic questions on ultraproducts of C~*-algebras and von Neumann al- gebras,including the relation to K-theory of C~*-algebras are considered.More specifically, we prove that under certain conditions,the K-groups of ultraproduct of C~*-algebras are iso- morphic to the ultraproduct of respective K-groups of C~*-algebras.We also show that the ultraproducts of factors of type Ⅱ_1 are prime,i.e.not isomorphic to any non-trivial tensor product.Some basic questions on ultraproducts of C*-algebras and yon Neumann algebras, including the relation to K-theory of C*-algebras are considered. More specifically,we prove that under certain conditions, the K-groups of ultraproduct of C*-algebras are isomorphic to the ultraproduct of respective K-groups of C*-algebras. We also show that the ultraproducts of factors of type Ⅱ1 are prime, i.e. not isomorphic to any non-trivial tensor product.

关 键 词：von NEUMANN algebras  C*-algebras  ultraproducts K-group  DOUBLE commutants. 

分 类 号：N[自然科学总论]