| 环上的广义导子与Von Neumann代数上的P-核值保持映射 |
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| 引用本文： | 朱军,熊昌萍.环上的广义导子与Von Neumann代数上的P-核值保持映射[J].数学学报,1998,41(4). |
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| 作者姓名： | 朱军 熊昌萍 |
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| 作者单位： | 湖北民族学院数学系 |
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| 基金项目： | 湖北省教委高校重点科研基金 |
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| 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．
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| 关 键 词： | Von Neumann代数，2－非绕的半素环．P－核值保持映射，广义导子，广义内导子 |
Generalized Derivations on Rings and Mappings of P-preserving Kernel into Range on Von Neumann Algebras |
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| Zhu Jun,Xiong Changping.Generalized Derivations on Rings and Mappings of P-preserving Kernel into Range on Von Neumann Algebras[J].Acta Mathematica Sinica,1998,41(4). |
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| Authors: | Zhu Jun Xiong Changping |
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| Institution: | Zhu Jun Xiong Changping (Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, China) |
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| Abstract: | Let A be an operator subalgebra in B(H), we say that a linear mapping ψ:AA 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. |
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| Keywords: | Von Neumann algebras 2-torsion free semiprime ring P-preserving kernel into range mapping Generalized derivation Generalized inner derivation |
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