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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17863 |
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| _version_ | 1866929230307131392 |
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| author | Mastnak, Mitja Radjavi, Heydar |
| author_facet | Mastnak, Mitja Radjavi, Heydar |
| contents | We prove that for any fixed unitary matrix $U$, any abelian self-adjoint algebra of matrices that is invariant under conjugation by $U$ can be embedded into a maximal abelian self-adjoint algebra that is still invariant under conjugation by $U$. We use this result to analyse the structure of matrices $A$ for which $A^*A$ commutes with $AA^*$, and to characterize matrices that are unitarily equivalent to weighted permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant embeddings and weighted permutations Mastnak, Mitja Radjavi, Heydar Rings and Algebras Functional Analysis 15A30 We prove that for any fixed unitary matrix $U$, any abelian self-adjoint algebra of matrices that is invariant under conjugation by $U$ can be embedded into a maximal abelian self-adjoint algebra that is still invariant under conjugation by $U$. We use this result to analyse the structure of matrices $A$ for which $A^*A$ commutes with $AA^*$, and to characterize matrices that are unitarily equivalent to weighted permutations. |
| title | Invariant embeddings and weighted permutations |
| topic | Rings and Algebras Functional Analysis 15A30 |
| url | https://arxiv.org/abs/2401.17863 |