(Real)linear preservers of multiples of unitaries and matrix pairs with some extremal norm properties
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912632463687680 |
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| author | Kuzma, Bojan Li, Chi-Kwong Poon, Edward |
| author_facet | Kuzma, Bojan Li, Chi-Kwong Poon, Edward |
| contents | We determine the structure of linear maps on complex (real) square matrices sending unitary (orthogonal) matrices to multiples of unitary (orthogonal) matrices. The result is used to determine the linear preservers of matrix pairs satisfying the extremal norm properties $\|AB\| = \|A\| \|B\|$, $\|A^*B\| = \|A\| \|B\|$, or $\|AB^*\| = \|A\| \|B\|$, for the spectral norm $\|\cdot\|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | (Real)linear preservers of multiples of unitaries and matrix pairs with some extremal norm properties Kuzma, Bojan Li, Chi-Kwong Poon, Edward Functional Analysis 15A60, 15A18, 15A86, 15A04 We determine the structure of linear maps on complex (real) square matrices sending unitary (orthogonal) matrices to multiples of unitary (orthogonal) matrices. The result is used to determine the linear preservers of matrix pairs satisfying the extremal norm properties $\|AB\| = \|A\| \|B\|$, $\|A^*B\| = \|A\| \|B\|$, or $\|AB^*\| = \|A\| \|B\|$, for the spectral norm $\|\cdot\|$. |
| title | (Real)linear preservers of multiples of unitaries and matrix pairs with some extremal norm properties |
| topic | Functional Analysis 15A60, 15A18, 15A86, 15A04 |
| url | https://arxiv.org/abs/2510.05303 |