Communications in Mathematical Physics

, Volume 40, Issue 3, pp 223–233 | Cite as

On the integral representation of states on a C*-algebra

  • Dang-Ngoc-Nghiem


The purpose of this paper is to give some complements to the various extremal decompositions of states on aC*-dynamical system i.e. a pair (A, G) whereA is aC*-algebra andG is a group acting on aA by *-automorphisms. We shall see for instance that the method of decomposition associated with a maximal abelianW*-algebra does not give all the extremal measures in the general case. We also give the explicit form of the greatest lower bound of all the extremal measures and a certain form of continuity of the decomposition. Finally we characterize various systems in the literature (G-abelian algebras, large systems and quasi-large systems) in terms of the equivalence of different notions of ergodicity.


Neural Network Dynamical System Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Dang-Ngoc-Nghiem
    • 1
  1. 1.Laboratoire de ProbabilitésUniversité Paris VIParisFrance

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