设H和K是复Hilbert空间, A和B分别是H和K上的因子von Neumann 代数. 本文给出了A和B的*-同构的一个特征, 设Φ:A→B是双射, 如果对任意A,B∈A,有Φ(A*B+B*A)=Φ(A)*(B)+Φ(B)*Φ(A),则Φ是线性或共轭线性*-同构.
Abstract
Let H and K be complex Hilbert spaces. Let A and B be two factor von Neumann algebras acting on H and K respectively. A characterization of *-isomorphism between A and B is given. Let Φ: A → B be a bijection. If Φ(A*B + B*A) = Φ(A)*Φ(B) + Φ(B)*Φ(A) for all A,B ∈ A, then Φ is a linear or a conjugate linear *-isomorphism.
关键词
因子von Neumann代数 /
Jordan同构 /
*-同构
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Key words
factor von Neumann algebra /
Jordan isomorphism /
*-isomorphism
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参考文献
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脚注
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基金
国家自然科学基金资助项目(11371233);中央高校基本科研业务费专项资金(GK201301007)
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