A linear mappingφfrom an algebra A into its bimodule M is called a centralizable mapping at G∈A ifφ(AB)=φ(A)B=Aφ(B)for each A and B in A with AB=G.In this paper,we prove that if M is a von Neumann algebra without...A linear mappingφfrom an algebra A into its bimodule M is called a centralizable mapping at G∈A ifφ(AB)=φ(A)B=Aφ(B)for each A and B in A with AB=G.In this paper,we prove that if M is a von Neumann algebra without direct summands of type I1 and type II,A is a*-subalgebra with M■A■LS(M)and G is a fixed element in A,then every continuous(with respect to the local measure topology t(M))centralizable mapping at G from A into M is a centralizer.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.1180100511801342+6 种基金118010041187102111801050)supported by a Startup Fundation of Anhui Polytechnic University(Grant No.2017YQQ017)supported by Shaanxi Provincial Education Department(Grant No.19JK0130)supported by Research Foundation of Chongqing Educational Committee(Grant No.KJQN2018000538)We would like to thank the for their patience and useful comments.
文摘A linear mappingφfrom an algebra A into its bimodule M is called a centralizable mapping at G∈A ifφ(AB)=φ(A)B=Aφ(B)for each A and B in A with AB=G.In this paper,we prove that if M is a von Neumann algebra without direct summands of type I1 and type II,A is a*-subalgebra with M■A■LS(M)and G is a fixed element in A,then every continuous(with respect to the local measure topology t(M))centralizable mapping at G from A into M is a centralizer.
