Quantumf-divergences in von Neumann algebras. II. Maximalf-divergences

  title={Quantumf-divergences in von Neumann algebras. II. Maximalf-divergences},
  author={Fumio Hiai},
  journal={Journal of Mathematical Physics},
  • Fumio Hiai
  • Published 9 July 2018
  • Computer Science, Mathematics
  • Journal of Mathematical Physics
As a continuation of the paper [20] 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 $L^1$-space, we present the general integral expression and the variational expression in terms of reverse tests. From these definition and expressions we prove important properties of maximal $f$-divergences, for instance, the monotonicity inequality, the joint… 
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