A Generalization of the Böttcher-Wenzel inequality for three rectangular matrices
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911077196890112 |
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| author | Nobori, Motoyuki |
| author_facet | Nobori, Motoyuki |
| contents | Let $m,n$ be positive integers. For all $m\times n$ complex matrices $A, C$ and an $n\times m$ matrix $B$, we define a generalized commutator as $ABC-CBA$. We estimate the Frobenius norm of it, and finally get the inequality, which is a generalization of the Böttcher-Wenzel inequality. If $n=1$ or $m=1$, then the Frobenius norm of $ABC-CBA$ can be estimated with a tighter upper bound. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalization of the Böttcher-Wenzel inequality for three rectangular matrices Nobori, Motoyuki Rings and Algebras Functional Analysis Operator Algebras 15A45, 15A60, 15A18 Let $m,n$ be positive integers. For all $m\times n$ complex matrices $A, C$ and an $n\times m$ matrix $B$, we define a generalized commutator as $ABC-CBA$. We estimate the Frobenius norm of it, and finally get the inequality, which is a generalization of the Böttcher-Wenzel inequality. If $n=1$ or $m=1$, then the Frobenius norm of $ABC-CBA$ can be estimated with a tighter upper bound. |
| title | A Generalization of the Böttcher-Wenzel inequality for three rectangular matrices |
| topic | Rings and Algebras Functional Analysis Operator Algebras 15A45, 15A60, 15A18 |
| url | https://arxiv.org/abs/2506.17365 |