ABSTRACT
In the present chapter, applying the inequalities between determinants and inverse operators, we obtain the norm estimates for the resolvent of a Schattenvon Neumann operator in terms of the distance from the complex parameter to the spectrum. These estimates enable us to obtain bounds for the spectral variations of bounded operators and investigate the perturbations of the eigenvectors. We also suggest an identity for resolvents which complements the Hilbert identity; that identity gives us additional perturbation results.
