The Moore-Penrose inverse and accretive operators with application to quadratic operator pencils

Abstract

We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application  we give a  factorization theorem for  a quadratic  pencil of accretive operators. Also, we study a result of existence, uniqueness, and maximal regularity of the strict solution  for complete abstract second order differential equation. The results are then used to discuss  a fourth order  linear boundary value problem. Illustrative examples are also given.