JournalsprimsVol. 11, No. 3pp. 809–833

Relative Entropy of States of von Neumann Algebras

  • Huzihiro Araki

    Kyoto University, Japan
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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