We determine the sharpest constant Cp,q,r​ such that for all complex
matrices X and Y, and for Schatten p-, q- and r-norms the inequality
∥XY−YX∥p​≤Cp,q,r​∥X∥q​∥Y∥r​ is valid. The main theoretical
tool in our investigations is complex interpolation theory.Comment: 32 pages, 88 picture