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| 套代数上的单位广义可导映射 | |
| 引用本文： | 张存侠. 套代数上的单位广义可导映射[J]. 纺织高校基础科学学报, 2008, 21(3): 317-319 |
| 作者姓名： | 张存侠 |
| 作者单位： | 陕西师范大学,数学与信息科学学院,陕西,西安,710062;陕西教育学院,数理工程系,陕西,西安,710061 |
| 摘 要： | 设τ（N）是一个原子套代数,φ是τ（N）到自身的线性映射.如果A,B∈τ（N）且AB=I,有（φAB）=φ（A）B＋Aφ（B）-Aφ（I）B,则称φ是τ（N）上的单位广义可导映射;如果 T,S∈τ（N）使得任意A∈τ（N）,有φ（A）=AT＋SA,则称φ是广义内导子.证明了原子套代数上的每个强算子拓扑连续的单位广义可导映射都是广义内导子. |
| 关 键 词： | 套代数 单位广义可导映射 广义导子 |
Generalized derivable mappings at unit operator on nest algebras |
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| ZHANG Cun-xia. Generalized derivable mappings at unit operator on nest algebras[J]. Basic Sciences Journal of Textile Universities, 2008, 21(3): 317-319 | |
| Authors: | ZHANG Cun-xia |
| Affiliation: | ZHANG Cun-scia (1. College of Mathematics and Information Science, Shaanxi Normal University,Xi＇an 710062, China; 2. Department of Maths, Physics and Engineering, Shaanxi Institute of Education, Xi＇an 710061, China) |
| Abstract: | If τ（N） is a atomic nest algebra, φ is a linear map from τ（N） to itself. If A↓A,B∈τ（N） and AB=I, then φ（AB）=φ（A）B＋Aφ（B）-Aφ（I）B, it is said that φ is a generalized derivable mapping at u-nit operator from τ（N） to itself. If there are T,S ∈τ（N） so that A↓A∈τ（N）, then φ（A） =AT＋SA, it is said that φ is a generalized inner derivation. It is proved that every strong operator topology continuous generalized derivable mapping at unit operator on any atomic nest algebra is a generalized inner derivation. |
| Keywords: | nest algebra generalized derivable mappings at unit operator generalized derivation |
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