Approximation and continuity of Moore–Penrose inverses of orthogonal row block matrices

A well-known result on the Moore–Penrose inverse of row block matrix asserts that [A,B]†=A†B† if and only if A∗B=0A∗B=0, where (·)†(·)† and (·)∗(·)∗ denote the Moore–Penrose inverse and the conjugate transpose of a matrix, respectively. In this paper, we show some norm inequalities for the difference [A,B]†-A†B†, and then use the norm inequalities to investigate approximation and continuity of [A,B]†[A,B]† as A∗B→0A∗B→0.