关于${1,3,4}$-逆的混合逆序律

In this paper, we study the mixed-type reverse order laws to {1, 3, 4}-inverses for closed range operators A, B and AB. It is shown that B{1, 3, 4}A{1, 3, 4} ?(AB){1, 3} if and only if R(A*AB) ? R(B). For every A(134)∈ A{1, 3, 4}, it has(A(134)AB){1, 3, 4}A{1, 3, 4} =(AB){1, 3, 4} if and only if R(AA*AB) ? R(AB). As an application of our results, some new characterizations of the mixed-type reverse order laws associated to the Moore-Penrose inverse and the {1, 3, 4}-inverse are established.