A Dimension-Independent Commutator Bound

Hao Shen, Jiaqi Wang, Lihong Zhi

We prove that every trace-zero matrix $A\in M_n(\mathbb{C})$ admits a representation $A=BC-CB$ with $B,C\in M_n(\mathbb{C})$ and $\Vert B\Vert \Vert C\Vert \le K\Vert A\Vert$,…