Perturbations of ground states of type 𝐼 𝐶*-algebras

Batty, C. J. K.

doi:10.1090/S0002-9939-1980-0556628-9

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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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