Communications in Mathematical Physics

, Volume 96, Issue 1, pp 1–13 | Cite as

Translation group and spectrum condition

  • H. -J. Borchers


Let {A, ℝ d ,α} be aC*-dynamical system, where ℝ d is thed-dimensional vector group. LetV be a convex cone in ℝ d and\(\hat V\) its dual cone. We will characterize those representations ofA with the properties (i)α a ,a∈ℝ d is weakly inner, (ii) the corresponding unitary representationU(a) is continuous, and (iii) the spectrum ofU(a) is contained in\(\hat V\).


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

© Springer-Verlag 1984

Authors and Affiliations

  • H. -J. Borchers
    • 1
  1. 1.Institut für Theoretische Physik der Universität GöttingenGöttingenFederal Republic of Germany

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