The expression of Moore--Penrose inverse of A-XY*

الأصل · EN

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 ∈ L(H) L(H,H) with R(A) closed and X,Y ∈ L(K,H) with R(X) R(A),R(Y) R(A*). In this short note, we give some new expressions of the Moore--Penrose inverse (A-XY*)+ of A-XY* under certain suitable conditions.