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arXiv · 2608.03897

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

Motoyuki Nobori
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Abstract

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 B\"{o}ttcher-Wenzel inequality.

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Motoyuki Nobori. 2026-08-04. A note on some upper bounds for the Frobenius norm of the $q$-deformed commutator. https://arxiv.org/abs/2608.03897

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