Publications of the Research Institute for Mathematical Sciences


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Volume 11, Issue 3, 1975, pp. 809–833
DOI: 10.2977/prims/1195191148

Relative Entropy of States of von Neumann Algebras

Huzihiro Araki (1)

(1) Kyoto University, 606-8502, KYOTO, JAPAN

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.

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