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Perturbations and ground states of $ C\sp \ast$-dynamical systems


Author: Hideki Kurose
Journal: Proc. Amer. Math. Soc. 95 (1985), 242-246
MSC: Primary 46L55; Secondary 46L40
DOI: https://doi.org/10.1090/S0002-9939-1985-0801331-5
MathSciNet review: 801331
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Abstract: In this paper we show that if a $ {C^ * }$-dynamical system has an irreducible covariant representation, every relatively bounded $ * $-derivation for its generator is also implemented by a relatively bounded selfadjoint operator for that associated with the dynamics. As its application, we assert that the existence of ground states of a $ {C^ * }$-dynamical system is stable under sufficiently small perturbations.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0801331-5
Keywords: $ {C^*}$-dynamical system, ground state, $ * $-derivation, perturbation
Article copyright: © Copyright 1985 American Mathematical Society

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