On Ando's inequalities for convex and concave functions

Koenraad M. R. Audenaert, Jaspal Singh Aujla

For positive semidefinite matrices $A$ and $B$, Ando and Zhan proved the inequalities $|||f(A)+f(B)|||\ge |||f(A+B)|||$ and $|||g(A)+g(B)|||\le |||g(A+B)|||$, for any uni…