Quantum f -divergences in von Neumann algebras. I. Standard f -divergences

Source abstract

We make a systematic study of standard f-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosaki’s variational expression of the relative entropy to an arbitrary standard f-divergence, from which most of the important properties of standard f-divergences follow immediately. In a similar manner, we give a comprehensive exposition on the Rényi divergence in von Neumann algebras. Some results on relative Hamiltonians formerly studied by Araki and Donald are improved as a by-product.