Norm inequalities related to operator monotone functions (Q1962565)

The authors prove that \[ |||f(A)+ f(B)|||\geq |||f(A+B)||| \] for \(A\), \(B\) positive semi-definite matrices and \(|||\cdot|||\) any unitarily invariant norm on the space of matrices, and for any nonnegative monotone function \(f(t)\) on \([0,\infty)\). They also establish that \[ |||g(A)+ g(B)|||\leq |||g(A+ B)||| \] for a nonnegative increasing function \(g(t)\) on \([0,\infty)\) with \(g(0)= 0\) and \(g(\infty)=\infty\) whose inverse function is operator monotone.