On matrix inequalities between the power means: counterexamples

Koenraad M. R. Audenaert, Fumio Hiai

We prove that the known sufficient conditions on the real parameters $(p,q)$ for which the matrix power mean inequality $((A^p+B^p)/2{)}^{1/p}\le ((A^q+B^q)/2{)}^{1/q}$ holds for every…