| 标准算子代数上保因子交换性的映射 |
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| 引用本文： | 焦美艳. 标准算子代数上保因子交换性的映射[J]. 数学研究及应用, 2013, 33(6): 708-716 |
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| 作者姓名： | 焦美艳 |
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| 作者单位： | 山西财经大学应用数学学院, 山西 太原 030006 |
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| 基金项目： | 国家自然科学基金 (Grant No.111101250),山西财经大学数学系科研创新基金. |
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| 摘 要： | Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar
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| 关 键 词： | 标准算子代数 交换性 因子 映射 Banach 单位元 复数 实数 |
| 收稿时间： | 2012-10-21 |
| 修稿时间： | 2013-07-07 |
Maps Preserving Commutativity up to a Factor on Standard Operator Algebras |
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| Meiyan JIAO. Maps Preserving Commutativity up to a Factor on Standard Operator Algebras[J]. Journal of Mathematical Research with Applications, 2013, 33(6): 708-716 |
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| Authors: | Meiyan JIAO |
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| Affiliation: | Department of Applied Mathematics, Shanxi University of Finance & Economics, Shanxi 030006, P. R. China |
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| Abstract: | Let $X$, $Y$ be real or complex Banach spaces with dimension greater than 2 and ${mathcal A}$, ${mathcal B}$ be standard operator algebras on $X$ and $Y$, respectively. Let $Phi:mathcal A rightarrow mathcal B$ be a unital surjective map. In this paper, we characterize the map $Phi$ on $mathcal A$ which satisfies $(A-B)R=xi R(A-B)Leftrightarrow (Phi(A)-Phi(B))Phi(R)=xiPhi(R)(Phi(A)-Phi(B))$ for $A,B,Rin mathcal A$ and for some scalar $xi$. |
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| Keywords: | preservers standard operator algebras commutativity up to a factor. |
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