| 标准算子代数上的Jordan映射 |
| |
| 引用本文： | 纪培胜,周淑娟.标准算子代数上的Jordan映射[J].数学研究及应用,2010,30(1):110-118. |
| |
| 作者姓名： | 纪培胜 周淑娟 |
| |
| 作者单位： | 青岛大学数学科学学院, 山东 青岛 266071;青岛大学数学科学学院, 山东 青岛 266071 |
| |
| 基金项目： | 国家自然科学基金(Grant Nos.10675086; 10971117);山东省自然科学基金(Grant No.Y2006A03). |
| |
| 摘 要： | Let A be a standard operator algebra on a Banach space of dimension 〉 1 and B be an arbitrary algebra over Q the field of rational numbers. Suppose that M ： A → B and M^＊ ： B → A are surjective maps such that {M（r（aM^＊（x）＋M^＊（x）a））=r（M（a）x＋xM（a））, M^＊（r（M（a）x＋xM（a）））=r（aM^＊（x）＋M^＊（x）a） for all a ∈ A, x ∈ B, where r is a fixed nonzero rational number. Then both M and M^＊ are additive.
|
| 关 键 词： | 标准算子代数 地图 Banach空间 约旦 有理数域 添加剂 立方 一维 |
| 收稿时间： | 1/6/2008 12:00:00 AM |
| 修稿时间： | 2008/4/16 0:00:00 |
Jordan Maps on Standard Operator Algebras |
| |
| Pei Sheng JI and Shu Juan ZHOU.Jordan Maps on Standard Operator Algebras[J].Journal of Mathematical Research with Applications,2010,30(1):110-118. |
| |
| Authors: | Pei Sheng JI and Shu Juan ZHOU |
| |
| Institution: | School of Mathematical Sciences,Qingdao University,Shandong 266071,P.R.China |
| |
| Abstract: | Let $A$ be a standard operator algebra on a Banach space of dimension $>1$ and $B$ be an arbitrary algebra over $Q$ the field of rational numbers. Suppose that $M:A\longrightarrow B$ and $M^*:B\longrightarrow A$ are surjective maps such that $$\left\{ \begin{array}{c}M(r(aM^*(x)+M^*(x)a))=r(M(a)x+xM(a)),\\M^*(r(M(a)x+xM(a)))=r(aM^*(x)+M^*(x)a)\end{array}\right.$$ for all $a\in A, x\in B$, where $r$ is a fixed nonzero rational number. Then both $M$ and $M^*$ are additive. |
| |
| Keywords: | Jordan maps standard operator algebras additivity |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
