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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Perturbations of ground states of type $\textrm {I}$ $C^{\ast }$-algebras
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by C. J. K. Batty
Proc. Amer. Math. Soc. 78 (1980), 539-544
DOI: https://doi.org/10.1090/S0002-9939-1980-0556628-9

Abstract:

It is shown that the class of irreducible representations of a type I ${C^\ast }$-algebra A which satisfy a spectrum condition for a given dynamical system on A is unchanged if the system undergoes a sufficiently small relatively bounded perturbation. It follows that if A is also unital, then the existence of ground states is unaffected by such perturbations.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 539-544
  • MSC: Primary 46L30; Secondary 81C12, 82A15
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0556628-9
  • MathSciNet review: 556628