  We give general spectral and eigenvalue perturbation bounds for a selfadjoint
operator perturbed in the sense of the pseudo-Friedrichs extension. We also
give several generalisations of the aforementioned extension. The spectral
bounds for finite eigenvalues are obtained by using analyticity and
monotonicity properties (rather than variational principles) and they are
general enough to include eigenvalues in gaps of the essential spectrum.
