This project is about operator monotonicity and operator convexity. These are related to important operations around mathematical physics modeled in the framework of operators on Hilbert spaces. A class of real functions f(x) called *operator monotone functions* exhibit strong convexity properties. This can be used to prove important convexity / concavity relations for von Neumann entropy and its variants. We plan to look at the theory of quantum f-divergence developed by Hiai, and improve known results (mostly about functions f(x) = x^p) to general operator monotone functions.
Prerequisite knowledge: