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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. DOI: 10.3770/j.issn:1000-341X.2010.01.010
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:2008-01-06
修稿时间:2008-04-16

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. DOI: 10.3770/j.issn:1000-341X.2010.01.010
Authors:Pei Sheng JI and Shu Juan ZHOU
Affiliation: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 $M:Alongrightarrow B$ 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.
Keywords:Jordan maps   standard operator algebras   additivity.
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