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Communications in Mathematical Physics

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

Translation group and spectrum condition

  • H. -J. Borchers
Article

Abstract

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\(\hat V\).

Keywords

Neural Network Dynamical System Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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