# Relative Entropy of States of von Neumann Algebras

### Huzihiro Araki

Kyoto University, Japan

## Abstract

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. 809–833

DOI 10.2977/PRIMS/1195191148