Linear maps preserving product of involutions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911523757096960 |
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| author | Li, Chi-Kwong Lohan, Tejbir Singla, Sushil |
| author_facet | Li, Chi-Kwong Lohan, Tejbir Singla, Sushil |
| contents | An element of the algebra $M_n(\mathbb{F})$ of $n \times n$ matrices over a field $\mathbb{F}$ is called an involution if its square equals the identity matrix. Gustafson, Halmos, and Radjavi proved that any product of involutions in $M_n(\mathbb{F})$ can be expressed as a product of at most four involutions. In this article, we investigate the bijective linear preservers of the sets of products of two, three, or four involutions in $M_n(\mathbb{F})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear maps preserving product of involutions Li, Chi-Kwong Lohan, Tejbir Singla, Sushil Functional Analysis Group Theory Operator Algebras Rings and Algebras Primary: 15A86, 15A23. Secondary: 20G15, 15A60. [2020] An element of the algebra $M_n(\mathbb{F})$ of $n \times n$ matrices over a field $\mathbb{F}$ is called an involution if its square equals the identity matrix. Gustafson, Halmos, and Radjavi proved that any product of involutions in $M_n(\mathbb{F})$ can be expressed as a product of at most four involutions. In this article, we investigate the bijective linear preservers of the sets of products of two, three, or four involutions in $M_n(\mathbb{F})$. |
| title | Linear maps preserving product of involutions |
| topic | Functional Analysis Group Theory Operator Algebras Rings and Algebras Primary: 15A86, 15A23. Secondary: 20G15, 15A60. [2020] |
| url | https://arxiv.org/abs/2504.14198 |