Characterizations of Centralizable Mappings on Algebras of Locally Measurable Operators  

作　　者：Jun HE Guang Yu AN Jian Kui LI Wen Hua QIAN 

机构地区：[1]Department of Mathematics,Anhui Polytechnic University,Wuhu 241000,P.R.China [2]Department of Mathematics,Shaanxi University of Science and Technology,Xi'an 710021,P.R.China [3]Department of Mathematics,East China University of Science and Technology,Shanghai 200237,P.R.China [4]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第9期1039-1048,共10页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11801005;11801342;11801004;11871021;11801050);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.

摘　　要：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.

关 键 词：Centralizable mapping CENTRALIZER von NEUMANN algebra LOCALLY measurable operator 

分 类 号：O15[理学—数学]