The expression of Moore--Penrose inverse of $A-X{Y}^{\ast }$

Fapeng Du, Yifeng Xue

Let $K,H$ be Hilbert spaces and let $L(K,H)$ denote the set of all bounded linear operators from $K$ to $H$. Let $A\in L(H)\triangleq L(H,H)$ with $R(A)$ closed and $X,Y \in L(K…