Perturbations of ground states of type $\textrm {I}$ $C^{\ast }$-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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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Keywords:
Type I <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^\ast }$">-algebra,
small perturbation,
ground state,
spectrum condition

Article copyright:
© Copyright 1980
American Mathematical Society