A Generalization of the Böttcher-Wenzel inequality for three rectangular matrices

Fuente: arXiv
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Main Author: Nobori, Motoyuki
Format: Preprint
Published: 2025
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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
id 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