Abstract
It is shown that K.M.S.-states are locally normal on a great number ofC*-algebras that may be of interest in Quantum Statistical Mechanics. The lattice structure and the Choquet-simplex structure of various sets of states are investigated. In this respect special attention is payed to the interplay of the K.M.S.-automorphism group with other automorphism groups under whose action K.M.S.-states are possibly invariant. A seemingly weaker notion thanG-abelianness of the algebra of observables, namelyG′-abelianness, is introduced and investigated. Finally a necessary and sufficient condition (on aC*-algebra with a sequential separable factor funnel) for decomposition of a locally normal state into locally normal states is given.
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Takesaki, M., Winnink, M. Local normality in Quantum Statistical Mechanics. Commun.Math. Phys. 30, 129–152 (1973). https://doi.org/10.1007/BF01645976
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DOI: https://doi.org/10.1007/BF01645976