Böttcher and Wenzel recently proved that for any unitarily invariant norm ∥· ∥, sup ∥XY-YX∥/ ∥XY∥ ∥X and aren×nnon-zero complex matrices=C≥2 and that C=2 when the norm is the Frobenius norm. They also asked whether the Frobenius norm is the only one having such property. In this paper, we answer the question by showing that the dual norm of the (2,2)-norm also has the property that C=2. © 2010 Elsevier Inc. All rights reserved.