On Eigenvalue and Eigenvector Estimates for Nonnegative Definite Operators

In this article we further develop a perturbation approach to the Rayleigh– Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of the theory to nonnegative definite operators . The perturbation argument enables us to solve two problems in one go: We determine which part of the spectrum of the operator is being approximated by the Ritz values and compute the approximation estimates. We also present a Temple–Kato like inequality which —unlike the original Temple–Kato inequality— applies to any test vectors from the quadratic form domain of the operator.