Sharp bounds for the operator norm of commutator


Che-Man Cheng, Ka Leong Hoi




Let ∥ · ∥ p denote the Schatten p-norm, 1 ≤ p ≤ ∞. The smallest constant C F ∞,q,r such that ∥XY − YX∥ ∞ ≤ C F ∞,q,r ∥X∥ q ∥Y∥ r for all real (F = R) or complex (F = C) matrices X and Y is determined.