Linear Preserver Problems
Linear Preserver Problems
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DOI：
10.1080/00029890.2001.11919790
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发表时间：
2001-08
期刊：
影响因子：
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通讯作者：
Chi-Kwong Li;S. Pierce
中科院分区：
文献类型：
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作者：
Chi-Kwong Li;S. Pierce
线性保持问题是矩阵算子理论中一个活跃的研究领域。这些问题涉及到矩阵或算子空间上的某些线性算子。我们在这篇文章中对这个主题作了一个概括性的介绍。在前三节中，我们将讨论动机、结果和问题。在最后三节中，我们描述了一些技术，概述了一些证明，并讨论了一些特殊的结果。1. 例子和典型问题。设Mm，n为m × n个复矩阵的集合，设Mn = Mn,n。设M， N∈Mn满足det(Mn) = 1。则映射φ: Mn→Mn由
Linear preserver problems is an active research area in matrix and operator theory. These problems involve certain linear operators on spaces of matrices or operators. We give a general introduction to the subject in this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss some exceptional results. 1. EXAMPLES AND TYPICAL PROBLEMS. Let Mm,n be the set of m × n complex matrices, and let Mn = Mn,n. Suppose that M, N ∈ Mn satisfy det( MN ) = 1. Then the mapping φ : Mn → Mn given by