A generalized reverse order law for the products of two operators
Guoxing Ji · Journal of Shaanxi Normal University · 2010
The reverse order law for {1,3,4}-inverse of the product of two operators is investigated by making full use of block-operator matrix technique and the representation for {1,3,4}-inverse of a linear bounded operator with closed range is given.Moreover,when R(A),R(B) and R(AB) are closed,it is proved that B{1,3,4}A{1,3,4}AB{1,3,4} if and only if R(A*AB)=R(B)(R(B)∩N(A)) and B*(R(B)∩N(A))=B+(R(B)∩N(A)).