Semi-centralizing maps of generalized matrix algebras☆
Semi-centralizing maps of generalized matrix algebras☆
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DOI：
10.1016/j.laa.2011.07.014
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发表时间：
2012-03
影响因子：
1.1
通讯作者：
Yanbo Li;F. Wei
中科院分区：
文献类型：
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作者：
Yanbo Li;F. Wei
本文在一定程度上是我们以前工作（Xiao和Wei（2010）[35]）的延续。受Brešar和Cheung的启发，我们将研究广义矩阵代数的半中心化映射，并通过常规而复杂的计算来描述它的一般形式。特别考虑了广义矩阵代数的斜交换映射和半中心化映射。证明了一类广义矩阵代数上的斜交换映射为零，广义矩阵代数上的半中心化导子为零。这些结果不仅为Brešar（2004）[6]的工作提供了新的视角，而且推广了Cheung（2001）[13]的主要结果。给出了一些与半中心化映射有关的应用。
The present article is a continuation of our former work (Xiao and Wei (2010) [35]) to some extent. Motivated by Brešar’s and Cheung’s wonderful ideas, we will study semi-centralizing maps of generalized matrix algebras and describe its general form by routine and complicated computations. Skew-commuting maps and semi-centralizing maps of generalized matrix algebras are specially considered. We prove that any skew-commuting map on a class of generalized matrix algebras is zero and that any semi-centralizing derivation on a generalized matrix algebra is zero. These results not only give new perspectives to the work of Brešar (2004) [6] but also extend the main results of Cheung (2001) [13]. A number of applications related to semi-centralizing maps are given.