An invariance property related to the mixed-type reverse order laws

Abstract

In this paper, we derive an interesting result that the mixed-type reverse order laws B{1, · · · }A{1, · · · } ⊆ (AB){1}hold if and only if the matrix product AB B (1,··· ) ··· ) is taken, respectively, as B (1)

An invariance property of operator products related to the mixed-type reverse order laws

“…Recently, two papers [9] and [10] cause us to be interested. The former discussed the reverse order laws for generalized inverses of two bounded linear operators using the matrix form of operator, and the latter presented invariance properties of matrix products related to the reverse order laws for two generalized inverses using the method of extremal ranks.…”