| 标准算子代数上的Jordan映射 |
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| 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. DOI: 10.3770/j.issn:1000-341X.2010.01.010 |
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| 作者姓名： | 纪培胜 周淑娟 |
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| 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 |
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| 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). |
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| 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.
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| 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： | 2008-01-06 |
| 修稿时间： | 2008-04-16 |
Jordan Maps on Standard Operator Algebras |
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| 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. DOI: 10.3770/j.issn:1000-341X.2010.01.010 |
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| Authors: | Pei Sheng JI and Shu Juan ZHOU |
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| Affiliation: | School of Mathematical Sciences,Qingdao University,Shandong 266071,P.R.China |
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| 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 $M:Alongrightarrow B$ and $M^*:Blongrightarrow A$ 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 $ain A, xin B$, where $r$ is a fixed nonzero rational number. Then both $M$ and $M^*$ are additive. |
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| Keywords: | Jordan maps standard operator algebras additivity. |
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