  We consider an Anderson impurity model in which the locally correlated
orbital is coupled to a host with a gapped density of states. Single-particle
dynamics are studied, within a perturbative framework that includes both
explicit second-order perturbation theory and self-consistent perturbation
theory to all orders in the interaction. Away from particle-hole symmetry the
system is shown to be a generalized Fermi liquid (GFL) in the sense of being
perturbatively connectable to the non-interacting limit; and the exact Friedel
sum rule for the GFL phase is obtained. We show by contrast that the
particle-hole symmetric point of the model is not perturbatively connected to
the non-interacting limit, and as such is a non-Fermi liquid for all non-zero
gaps. Our conclusions are in agreement with NRG studies of the problem.
