Note on the Invariance Properties of Operator Products Involving Generalized Inverses

Abstract

We investigate further the invariance properties of the bounded linear operator product ${AC}^{\left(1\right)} B^{\left(1\right)} D$ and its range with respect to the choice of the generalized inverses $X$ and $Y$ of bounded linear operators. Also, we discuss the range inclusion invariance properties of the operator product involving generalized inverses.