Proof of Böttcher and Wenzel's conjecture on commutator norms for 3-by-3 matrices (Q875018)

The author proves that \[ \left| \left| AX-XA\right| \right| _{F}\leq \sqrt{2} \left| \left| A\right| \right| _{F}\left| \left| X\right| \right| _{F} \] for all \(3\times 3\) matrices, where \(\left| \left| \cdot \right| \right| _{F}\) is the Frobenius norm. This inequality is a particular case of the general inequality given in the conjecture of \textit{A. Böttcher} and \textit{D. Wenzel} [ibid. 403, 216--228 (2005; Zbl 1077.15020)].