Key points are not available for this paper at this time.
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.
Huzihiro Araki (Wed,) studied this question.