On Schatten p-norms of commutators

For any odd integer d >= 3, we determine the sharpest constant C-p,C-g,C-r such that parallel to XY - YX parallel to(p) <= ;C-p,C-q,C-r parallel to X parallel to(q)parallel to Y parallel to(r) for all X, Y is an element of M-d, where M-d denotes the set of all d x d complex matrices, parallel to center dot parallel to(p), 1 <= p <= infinity, denotes the Schatten p-norm on M-d, and 1 <= p, q, r <= infinity satisfy 1/p >1/q + 1/r. This is a continuation of the study of the problem considered in Wenzel and Audenaert (2010) [8]. (C) 2015 Elsevier Inc. All rights reserved.