利用算子分块矩阵的技巧,研究了两个算子乘积的{1,3,4}逆的广义逆序律,证明了当R(A)、R(B)以及R(AB)都闭时,(AB){1,3,4}=B{1,3,4}.A{1,3,4}当且仅当R(B)=R(A*AB),或者R(A*)R(B)且B*(R(B)∩N(A))=B+(R(B)∩N(A))。
The reverse order law for {1,3,4}-inverse of the product of two operators is investigated by using the technique of block-operator matrix and when R(A)、R(B)、R(AB) are closed.It is proved that(AB){1,3,4}=B{1,3,4}·A{1,3,4} if and only if R(B)=R(A*AB),or R(A*)R(B) and B*(R(B)∩N(A))=B+(R(B)∩N(A)).