环上的广义导子与Von Neumann代数上的P-核值保持映射  

Generalized Derivations on Rings and Mappings of P-preserving Kernel into Range on Von Neumann Algebras

作　　者：朱军[1] 熊昌萍[1] 

机构地区：[1]湖北民族学院数学系

出　　处：《数学学报（中文版）》1998年第4期795-800,共6页Acta Mathematica Sinica：Chinese Series

基　　金：湖北省教委高校重点科研基金

摘　　要：设Ａ是Ｂ（Ｈ）的子代数，ψ是Ａ到Ａ的线性映射，且对Ａ中的每个正交投影算子ｐ，有ψ（ｐ）（ｋｅｒｐ）ｒａｎｐ，则称ψ是Ａ到Ａ的Ｐ－核值保持映射，本文主要得到如下结果：每个２－非绕的半素环上的广义Ｊｏｒｄａｎ导子都是广义导子；每个ＶｏｎＮｅｕｍａｎｎ代数上的范数拓扑连续的Ｐ－核值保持映射是广义内导子．Let A be an operator subalgebra in B(H), we say that a linear mapping ψ:AA is a P-pre serving kernel into range mapping if ψ(p)( ker p)  ran p for any self-adjoint projection operator p in A. In this paper, we obtain the following main results: Every generalized Jordan derivation on 2-torsion free semiprime rings is a generalized derivation; Every norm-continuous linear mapping of P-preserving kernel into range on Von Neumann algebras is a generalized inner derivation.

关 键 词：NEUMANN代数 P-核值保持映射 广义导子 环 

分 类 号：O177.5[理学—数学]