Invariant embeddings and weighted permutations

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/proc/16835

M. Mastnak, H. Radjavi

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引用次数: 0

Abstract

We prove that for any fixed unitary matrix U U , any abelian self-adjoint algebra of matrices that is invariant under conjugation by U U can be embedded into a maximal abelian self-adjoint algebra that is still invariant under conjugation by U U . We use this result to analyse the structure of matrices A A for which A ∗ A A^*A commutes with A A ∗ AA^* , and to characterize matrices that are unitarily equivalent to weighted permutations.

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不变嵌入和加权排列

我们证明，对于任何固定的单元矩阵 U U，任何在 U U 共轭下不变的矩阵无边自交代数都可以嵌入到一个在 U U 共轭下仍然不变的最大无边自交代数中。我们利用这一结果来分析 A ∗ A A^*A 与 A A ∗ AA^* 共轭的矩阵 A A 的结构，并描述与加权排列单元等价的矩阵的特征。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.