Perturbations and ground states of 𝐶*-dynamical systems

Abstract

In this paper we show that if a C ∗ {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 ∗ {C^ * } -dynamical system is stable under sufficiently small perturbations.