Perturbations of ground states of type -algebras

Author:
C. J. K. Batty

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

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the class of irreducible representations of a type I -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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0556628-9

Keywords:
Type I -algebra,
small perturbation,
ground state,
spectrum condition

Article copyright:
© Copyright 1980
American Mathematical Society