arXiv subjects

Motoyuki Nobori

Publications and source records attributed to Motoyuki Nobori.

2 recordsLinked to original sources

arXiv2026

A note on some upper bounds for the Frobenius norm of the $q$-deformed commutator

For two square complex matrices $A,B,$ and a real number $q$, the $q$-deformed commutator of $A$ and $B$ is defined as $AB-qBA$. We give some upper bounds on the Frobenius norm of the $q$-deformed commutator in the case $q\ge0$. All of the inequalities derived in this paper generalize the Böttcher-Wenzel inequality.

math.RA↗

arXiv2025

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

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.

math.RA↗