Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 323 / 3 / ii / a

A real function $f$ on $I=[0,1]$ is an operator convex function when, for all Hermitian operators $X,Y$ whose spectra lie in $I$ and every $0\le \lambda \le 1$,where $⪯$ is the Loewner order. Reversing the inequality defines an operator concave function, equivalently $-f$ is operator convex.