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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Perturbations of ground states of type $ {\rm I}$ $ C\sp{\ast} $-algebras


Author: C. J. K. Batty
Journal: Proc. Amer. Math. Soc. 78 (1980), 539-544
MSC: Primary 46L30; Secondary 81C12, 82A15
MathSciNet review: 556628
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0556628-9
PII: S 0002-9939(1980)0556628-9
Keywords: Type I $ {C^\ast}$-algebra, small perturbation, ground state, spectrum condition
Article copyright: © Copyright 1980 American Mathematical Society