  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.
