| 李倩,李鹏同.完全分配CSL代数上的中心化子[J].数学年刊A辑,2011,32(3):375~384 |
| 完全分配CSL代数上的中心化子 |
| Centralizers of Completely Distributive CSL Algebras |
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| DOI： |
| 中文关键词: 完全分配CSL代数 中心化子 Jordan中心化子 Lie中心化子 |
| 英文关键词:Completely distributive CSL algebra Centralizer Jordan centralizer Lie centralizer |
| 基金项目:国家自然科学基金(No.10771101)资助的项目 |
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| 中文摘要: |
| 设$\mathcal L$是可分Hilbert空间上的完全分配交换子空间格, $\mathcal A$是${\rm Alg}\, \mathcal L$的子代数并且包含${\rm Alg}\, \mathcal L$的全体有限秩算子.
主要结果是: (1) $\mathcal A$上的中心化子是拟空间的; (2) ${\rm Alg}\, \mathcal L$上的Jordan中心化子是中心化子; (3) 当$\mathcal L$是套时,
${\rm Alg}\, \mathcal L$上的Lie中心化子可表示成一个中心化子与一个可加泛函之和的形式, 该泛函作用在形如$AB-BA$的算子上为零. |
| 英文摘要: |
| Let $\mathcal L$ be a completely distributive commutative subspace lattice on a separable Hilbert space, $\mathcal A$ be a subalgebra of ${\rm Alg}\, \mathcal L$
which contains all finite rank operators in ${\rm Alg}\, \mathcal L$. The main results are as follows: (1) Every centralizer of $\mathcal A$ is
quasi-spatial; (2) Every Jordan centralizer of ${\rm Alg}\, \mathcal L$ must be a centralizer; (3) If $\mathcal L$ is a nest, then every Lie centralizer of
${\rm Alg}\, \mathcal L$ can be written as a sum of a centralizer and an additive functional on the nest algebra,
where the additive functional
annihilates operators of the form $AB-BA$. |
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