On α-z-Rényi divergence in the von Neumann algebra setting

Abstract

We will investigate the α-z-Rényi divergence in the general von Neumann algebra setting based on Haagerup non-commutative Lp-spaces. In particular, we establish almost all its expected properties when 0 < α < 1 and some of them when α > 1. In an Appendix we also give an equality condition for generalized Hölder’s inequality in Haagerup non-commutative Lp-spaces.