$M_n(\mathbb C)$ 中部分等距的序自同构
Order automorphisms of partial isometries in $M_n(\mathbb C)$
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中文总结 AI 辅助
本文刻画了矩阵代数中部分等距集合上的序自同构，发现其无法由标准可逆或酉变换实现，而由 $I-(A+A^*)$ 正或负可逆的矩阵支配，结构比经典子空间自同构更复杂。
中文摘要 AI 辅助
我们研究并刻画了有限维矩阵代数 $M_n(\mathbb{C})$ 中部分等距集合上的序自同构。与子空间格的经典序自同构不同（后者可由标准可逆或酉变换实现），此处考虑的序自同构不具有此类常规矩阵表示。相反，它们本质上由满足 $I-(A+A^*)$ 为正或负可逆的矩阵所支配。结果表明，部分等距的序自同构的结构特征比经典子空间自同构要复杂得多。
英文摘要
We investigate and characterize order automorphisms on the set of partial isometries in the finite-dimensional matrix algebra $M_n(\mathbb{C})$. Different from the classical order automorphisms of subspace lattices, which can be implemented by standard invertible or unitary transformations, the order automorphisms considered herein admit no such conventional matrix representations. Instead, they are essentially governed by matrices such that $I-(A+A^*)$ is either positive or negative invertible. The results reveal that the structural features of order automorphisms for partial isometries are substantially more intricate than those of classical subspace automorphisms.
发表机构
- School of Mathematics and Statistics, Shaanxi Normal University（陕西师范大学数学与统计学院）
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