A factorization of a quadratic pencils of accretive operators and applications

TL;DR

This paper presents a canonical factorization for quadratic pencils of accretive operators in Hilbert spaces, explores relationships with Moore-Penrose inverses, and applies these results to establish existence and regularity of solutions for second order differential equations.

Contribution

It introduces a new canonical factorization for quadratic pencils of accretive operators and connects it with Moore-Penrose inverses, advancing the theory of operator equations and differential equations.

Findings

Canonical factorization for quadratic pencils of accretive operators

Relationships between m-accretive operators and Moore-Penrose inverses

Existence, uniqueness, and maximal regularity of solutions for second order differential equations

Abstract

A canonical factorization is given for a quadratic pencil of accretive operators in a Hilbert space. Also, we establish some relationships between an m-accretive operator and its Moore-Penorse inverse. As an application, we study a result of existence, uniqueness, and maximal regularity of the strict solution for complete abstract second order differential equation in the non-homogeneous case. The paper is concluded with some questions left open from the preceding discussions.