Abstract:
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)).
