Integral Criteria for the Quality of the Dichotomy of a Matrix Spectrum by a Closed Contour

A well-known method for estimating the sensitivity of invariant projection operators, which is based on the dichotomy quality integral criteria and is oriented to perturbations of general form, is extended to the case of regularly structured perturbations. For finite-dimensional approximations of differential operators, this allows us, in particular, to obtain significantly more precise estimates of the sensitivity of invariant projection operators (corresponding to the eigenvalues minimal in absolute value) to perturbations of the coefficients of these operators. We give a new definition of the dichotomy quality integral criteria as the $L_p$ -norm of the resolvent, which allows us to simplify the proofs and to formulate the final results in a more general and simpler form.