Providing valuable new tools for specialists in functional analysis and stability theory, this state-of-the-art reference presents a systematic exposition of estimations for norms of operator-valued functions and applies the estimates to spectrum perturbations of linear operators and stability theory. Demonstrating a novel approach to spectrum perturbations, Norm Estimations for Operator-Valued Functions and Applications considers a common procedure for the stability analysis of various classes of equations extends the well-known spectrum perturbation result for self-adjoint operators to quasi-Hermitian operators examines spectrum perturbations of operators on a tensor product of Hilbert spaces covers systems of ordinary differential equations deal with retarded systems studies the absolute stability of systems of Volterra equations emphasizes semilinear evolution equations and more!