J -子空间格代数上中心化子和广义导子的刻画

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 463-472.

• 论文 • 上一篇

J -子空间格代数上中心化子和广义导子的刻画

齐霄霏

山西大学数学科学学院太原 030006

收稿日期:2012-06-26 修回日期:2013-09-15 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
国家自然科学基金(11101250)和山西省青年科技基金(2012021004) 资助.

Characterization of Centralizers and Generalized Derivations on J-Subspace Lattice Algebras

QI Xiao-Fei

School of Mathematics, Shanxi University, Taiyuan 030006

Received:2012-06-26 Revised:2013-09-15 Online:2014-04-25 Published:2014-04-25
Supported by:
国家自然科学基金(11101250)和山西省青年科技基金(2012021004) 资助.

摘要/Abstract

摘要：

设L是Banach空间X上的J -子空间格, AlgL是相应的J -子空间格代数. 设Φ: AlgL→AlgL是可加映射, 对每个K∈J(L), dimK≥2. 该文证明了下列表述等价: (1) Φ是中心化子; (2) Φ满足AB=0→Φ(A)B=AΦ(B)=0; (3) Φ满足AB+BA=0→Φ(A)B+Φ(B)A=AΦ(B)+B\Φ(A)=0; (4) Φ满足ABC+CBA=0→Φ(A)BC+Φ(C)BA=ABΦ(C)+CBΦ(A)=0. 作为应用, 得到AlgL上在零点广义可导的可加映射的完全刻画.

关键词: J -子空间格代数, 中心化子, 广义导子

Abstract:

Let L be a J-subspace lattice on a Banach space X and AlgL the associated J-subspace lattice algebra. Assume that Φ: AlgL→AlgL is an additive map and dimK≥2 for every K∈J(L). It is shown that the following statements are equivalent: (1) Φ is a centralizer; (2) Φ sataisies Φ(A)B=AΦ(B)=0 whenever A, B∈AlgL with AB=0; (3) Φ satisfies Φ(A)B+Φ(B)A=AΦ(B)+B\Φ(A)=0 whenever A, B∈AlgL with AB+BA=0; (4) Φ satisfies Φ(A)BC+Φ(C)BA=ABΦ(C)+CBΦ(A)=0 whenever A, B∈AlgL with ABC+CBA=0. As an application, additive maps generalized derivable at zero on AlgL are characterized.

Key words: J-subspace lattice algebras, Centralizers, Generalized derivations

中图分类号:

47L35

齐霄霏. J -子空间格代数上中心化子和广义导子的刻画[J]. 数学物理学报, 2014, 34(2): 463-472.

QI Xiao-Fei. Characterization of Centralizers and Generalized Derivations on J-Subspace Lattice Algebras[J]. Acta mathematica scientia,Series A, 2014, 34(2): 463-472.

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J -子空间格代数上中心化子和广义导子的刻画

Characterization of Centralizers and Generalized Derivations on J-Subspace Lattice Algebras

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