Von Neumann代数套子代数上保因子交换性的线性映射

焦美艳

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 409-416.

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数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 409-416. DOI: 10.12386/A2014sxxb0040
论文

Von Neumann代数套子代数上保因子交换性的线性映射

    焦美艳
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Linear Maps Preserving Commutativity up to a Factor on Nest Subalgebras of Von Neumann Algebras

    Mei Yan JIAO
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摘要

对因子von Neumann代数的套子代数上的保单位线性映射Φ：AlgMα → AlgMβ满足AB=ζ BA⇔ Φ（A）Φ（B）=ζΦ（B）Φ（A）进行了刻画，其中A，B∈ AlgMα，ζ∈F，即证明了因子vonNeumann代数的套子代数间每个保单位的弱连续线性满射它双边保因子交换性，则映射Φ或者是同构或者是反同构.

Abstract

We characterize the linear map Φ: AlgMα → AlgMβ which statisfies the property that Φ(I) = I and AB = ζBA ⇔ Φ(A)Φ(B) = ζΦ(B)Φ(A) for A,B ∈ AlgMα and for some scalar ζ. It is proved that every surjective weakly continuous linear map preserving identity and commutativity up to a factor in both directions between two nest subalgebras with non-trivial nests of any factor von Neumann algebra is either an isomorphism or an anti-isomorphism.

关键词

线性保持 / 因子交换性 / von Neumann 代数 / 套子代数

Key words

linear preserver / commutativity up to a factor / von Neumann algebra / nest subalgebra

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焦美艳. Von Neumann代数套子代数上保因子交换性的线性映射. 数学学报, 2014, 57(2): 409-416 https://doi.org/10.12386/A2014sxxb0040
Mei Yan JIAO. Linear Maps Preserving Commutativity up to a Factor on Nest Subalgebras of Von Neumann Algebras. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 409-416 https://doi.org/10.12386/A2014sxxb0040

参考文献

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基金

国家自然科学青年基金资助项目（111101250）；山西财经大学应用数学学院科研创新团队基金及山西财经大学青年基金资助项目
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