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},...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.展开更多
In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are ...In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1150134511671261)the Youth Backbone Teacher Training Program of Henan Province(Grant No.2017GGJS140)
文摘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.
文摘In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.
