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Translation group and spectrum condition

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Abstract

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

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Authors and Affiliations

  1. Institut für Theoretische Physik der Universität Göttingen, Bunsenstr. 9, D-3400, Göttingen, Federal Republic of Germany

    H. -J. Borchers

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  1. H. -J. Borchers
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Communicated by H. Araki

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Borchers, H.J. Translation group and spectrum condition. Commun.Math. Phys. 96, 1–13 (1984). https://doi.org/10.1007/BF01217346

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  • DOI: https://doi.org/10.1007/BF01217346

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