Bounds on Perturbations of Self-Adjoint Operators

An improvement of a perturbation theory lemma by M. M. Skriganov which gives an upper bound to the shift of eigenvalues is presented along with other related theorems. These results are also compared with Temple’s inequality and the generalized Temple’s inequality. Applications to spectral theory of differential operators, inverse spectral theory, and quantum mechanics are included. In conjunction with the Rayleigh-Ritz method, a method for bracketing the eigenvalues is developed.