Relative Entropy of States of von Neumann Algebras

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. © 1976, Research Institute for Mathematical Sciences. All rights reserved.