| Nest代数上的在零点广义可导映射 |
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| 引用本文： | 朱军,熊昌萍.Nest代数上的在零点广义可导映射[J].数学学报,2002,45(4):783-788. |
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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,湖北,恩施,445000 |
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| 基金项目： | 湖北省自然科学基金资助项目，湖北省教委高校重点科研基金资助项目 |
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| 摘 要： | 设A为B（H）的子代数, 是A到B（H）的线性映射,我们说 在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有 （ST）= （S）T+S （T）-S （I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_ H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.
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| 关 键 词： | Nest代数 广义内导子 在0点广义可导映射 在0点广义双边可导映射 核值保持映射 |
| 文章编号： | 0583-1431(2002)04-0783-06 |
| 修稿时间： | 1999年6月28日 |
Generalized Derivable Mappings at the Point Zero on Nest Algebras |
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| Jun ZHU,Chang Ping XIONG.Generalized Derivable Mappings at the Point Zero on Nest Algebras[J].Acta Mathematica Sinica,2002,45(4):783-788. |
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| Authors: | Jun ZHU Chang Ping XIONG |
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| Institution: | Jun ZHU Chang Ping XIONG(Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, P. R. China) (Fax: (0718)8431176; E-mail: e3zj105@public.es.hb.cn) |
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| Abstract: | Let A be a subalgebra of B(H), we say that a linear mapping : A→B(H) is a generalized derivable (generalized biderivable) at the point zero if (ST) = (S)T+ S (T) - S(I)T for any S, T ∈ A with ST = 0 (ST = 0 or TS = 0). In this paper, we obtain the following results: (1) Every norm-continuous linear mapping of generalized derivable at the point zero on finite nest algebras is a generalized inner derivation; (2) Let N be a complete nest with H_ H, then every norm-continuous linear mapping of generalized biderivable at the point zero on the nest algebra alg N is a generalized inner derivation. |
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| Keywords: | Nest algebra Generalized inner derivation Generalized derivable mapping at the point zero Generalized biderivable at the point zero Mapping of preserving kernel into range |
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