Quantum f -divergences in von Neumann algebras. II. Maximal f -divergences
Fumio Hiai
Source abstract
As a continuation of the study by Hiai [J. Math. Phys. 59, 102202 (2018)] on standard f-divergences, we make a systematic study of maximal f-divergences in general von Neumann algebras. For maximal f-divergences, apart from their definition based on Haagerup’s L1-space, we present the general integral expression and the variational expression in terms of reverse tests. From these expressions as well as the definition, we prove important properties of maximal f-divergences, for instance, the monotonicity inequality, the joint convexity, the lower semicontinuity, and the martingale convergence. The inequality between the standard and the maximal f-divergences is also given.
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