  The energy eigenvalues of the class of non-Hermitian PT-symmetric
Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) are real, positive, and
discrete. The behavior of these eigenvalues has been studied perturbatively for
small $\epsilon$. However, until now no other features of $H$ have been
examined perturbatively. In this paper the small-$\epsilon$ expansion of the C
operator and the equivalent isospectral Dirac-Hermitian Hamiltonian $h$ are
derived.
