| 算子代数上的初等映射 |
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| 引用本文： | 安润玲,侯晋川. 算子代数上的初等映射[J]. 山西大学学报(自然科学版), 2009, 32(3) |
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| 作者姓名： | 安润玲 侯晋川 |
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| 作者单位： | 太原理工大学数学系,山西,太原,030024 |
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| 基金项目： | 数学天元基金，国家自然科学基金 |
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| 摘 要： | 设(R)和(R)'为给定的两个环,映射M:(R) → (R)'和M*:(R)'→(R)是满射且满足{M(AM*(B)C)=M(A)BM(C) M*(BM(A)D)=M*(B)AM*(D)(V)A,C∈(R),(V)B,D∈(R) 在一定条件下证明了存在环同构N:(R)→(R)'使得M(A)=N(A)M(I),M*(B)=N-1(BM(I)).利用此结论将刻画(X)上的初等映射.
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| 关 键 词： | 初等映射 环同构 套代数 |
Elementary Maps on Operator Algebras |
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| AN Run-ling,HOU Jin-chuan. Elementary Maps on Operator Algebras[J]. Journal of Shanxi University (Natural Science Edit, 2009, 32(3) |
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| Authors: | AN Run-ling HOU Jin-chuan |
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| Affiliation: | AN Run-ling,HOU Jin-chuan(Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | Let (R) and (R) be two rings. Under some assumptions on (R) and (R)', we show that if maps M:(R)→(R)' and M~* :(R)'→(R) are surjective and satisfy｛M(AM~*(B)C)=M(A)BM(C)M~* (BM(A)D) = M~* (B)AM~* (D) (A)A,C∈(R),(A)B,D∈(R)'then there is a ring isomorphism N such that M(A) = N(A)M(I) and M~* (B) = N~(-1)(BM( I)). As its applications, we give a characterization of such maps on (R)(X). |
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| Keywords: | elementary maps ring isomorphism nest algebras |
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