Vol. 96, No. 1, 1981

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Sufficiency, KMS condition and relative entropy in von Neumann algebras

Fumio Hiai, Masanori Ohya and Makoto Tsukada

Vol. 96 (1981), No. 1, 99–109
Abstract

The sufficiency in von Neumann algebras is discussed with some applications to classification of normal states. It is shown that the concept of sufficiency characterizes the KMS-states and the invariant states with respect to a modular automorphism group. The relations between the sufficiency and the relative entropy are established.

Mathematical Subject Classification 2000
Primary: 46L30
Milestones
Received: 13 March 1979
Revised: 4 January 1980
Published: 1 September 1981
Authors
Fumio Hiai
Masanori Ohya
Makoto Tsukada