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 |
标准算子代数上的Jordan映射 |
Jordan Maps on Standard Operator Algebras |
投稿时间:2008-01-06 修订日期:2008-04-16 |
DOI:10.3770/j.issn:1000-341X.2010.01.010 |
中文关键词: Jordan映射 标准算子代数 可加性. |
英文关键词:Jordan maps standard operator algebras additivity. |
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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中文摘要: |
设$A$是维数 $>1$的Banach空间上的标准算子代数,$B$有理数域$Q$上的代数. 如果满射 $M:A\longrightarrow B$和$M^*:B\longrightarrow A$满足任给$a\in A, x\in B$都有$$\left\{ \begin{array}{c}M(r(aM^*(x) M^*(x)a))=r(M(a)x xM(a)),\\M^*(r(M(a)x xM(a)))=r(aM^*(x) M^*(x)a),\end{array}\right$$其中$r$是给定的非零有 |
英文摘要: |
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 $M:A\longrightarrow B$ 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. |
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