Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved for general von Neumann algebra.
Cite this article
Huzihiro Araki, Relative Entropy of States of von Neumann Algebras. Publ. Res. Inst. Math. Sci. 11 (1975), no. 3, pp. 809–833DOI 10.2977/PRIMS/1195191148