JournalsprimsVol. 11 , No. 3DOI 10.2977/prims/1195191148

Relative Entropy of States of von Neumann Algebras

  • Huzihiro Araki

    Kyoto University, Japan
Relative Entropy of States of von Neumann Algebras cover

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.