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| 广义反导子的刻画 | |
| 引用本文： | 霍东华,刘红玉,郑宝东. 广义反导子的刻画[J]. 哈尔滨理工大学学报, 2012, 17(3): 42-45 |
| 作者姓名： | 霍东华 刘红玉 郑宝东 |
| 作者单位： | 1. 牡丹江师范学院数学系,黑龙江牡丹江157012;哈尔滨工业大学理学院,黑龙江哈尔滨150001 2. 牡丹江师范学院数学系,黑龙江牡丹江,157012 3. 哈尔滨工业大学理学院,黑龙江哈尔滨,150001 |
| 基金项目： | 黑龙江省教育厅科学技术研究项目(面上项目)，牡丹江师范学院科学技术研究项目 |
| 摘 要： | 为了深入研究导子的问题,利用类比的方式给出广义反导子的定义,并研究广义反导子和反导子之间的关系.最后利用零积的性质对它进行刻画.结论是设A是一个Banach代数具有性质(C),且有有界的近似单位元,X是一个Banach A-双模满足{x∈X:axb=0,a,b∈Z(A)}={0}.δ是A到X的一个连续的线性算子满足a,b,c∈A,ab=bc=0■c.δ(b).a=0,则δ是一个广义反导子. |
| 关 键 词： | Banach代数 反导子 广义反导子 |
Characterizations of Generalized Antiderivations |
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| HUO Dong-hua , LIU Hong-yu , ZHENG Bao-dong. Characterizations of Generalized Antiderivations[J]. Journal of Harbin University of Science and Technology, 2012, 17(3): 42-45 | |
| Authors: | HUO Dong-hua LIU Hong-yu ZHENG Bao-dong |
| Affiliation: | 1Mudanjiang Normal University,Department of Mathematics,Mudanjiang 157012,China; 2.College of Mathematies,Harbin Institute of Technology,Harbin 150001,China) |
| Abstract: | In order to further study of derivation,this paper introduces generalized antiderivation definition using the analogy method,and then it gives the relationship between generalized antiderivation and antiderivation.Finaly,it characterizes the generalized antiderivation though zero product properties.The conclusion is that let A be a Banach algebra with the property(C) and having a bounded approximate identity,let X be Banach A-bimodule such that {x∈X:axb=0,a,b∈Z(A)}={0},and let δ:A→X be a continuous linear operator satisfying a,b,c∈A,ab=bc=0■c·δ(b)·a=0,then δ is a generalized derivation. |
| Keywords: | Banach algebra antiderivation generalized antiderivation |
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