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Functional Dependence Between The Hamiltonian And The Modular Operator Associated With A Faithful Invariant State Of A W*-Dynamical System

J. Canniére
Published 1984 · Mathematics

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Let H and A be the hamiltonian, resp. the modular operator associated with an invariant faithful normal state w of a W^*-dynamical system (A, a). Then J =/(//) for some decreasing function f if and only if (roughly speaking) w is 2-passive with respect to a. It follows that under certain conditions a 3-passive state is an equilibrium (i.e. KMS) state.
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