Structure of the spaces of matrix monotone functions and of matrix convex functions and Jensen's type inequality for operators

Hiroyuki Osaka, Jun Tomiyama

Let $n\in \mathbb{N}$ and $M_n$ be the algebra of $n\times n$ matrices. We call a function $f$ matrix monotone of order $n$ or $n$-monotone in short whenever the inequality $f(a) \leq f(…