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

TL;DR

This paper explores properties of the Moore-Penrose inverse of accretive operators, providing new perturbation results, a factorization theorem for quadratic operator pencils, and conditions for solutions of second order differential equations.

Contribution

It introduces novel relationships and perturbation results for the Moore-Penrose inverse of accretive operators, and applies these to quadratic operator pencils and differential equations.

Findings

Established relationships between accretive operators and their Moore-Penrose inverses.

Derived perturbation results for the Moore-Penrose inverse of maximal accretive operators.

Provided a factorization theorem for quadratic pencils of accretive operators.

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. Illustrative examples are also given.