算子乘积的{1,2,3}-逆逆序律

Reverse Order Laws for {1,2,3}-inverse of Two-operator Product

借助特殊的空间分解,研究算子乘积的广义逆序律问题,给出当算子A、B、AB为闭值域算子时,B{1,2,3}A{1,2,3}=AB{1,2,3}和B{1,2,4}A{1,2,4}=AB{1,2,4}分别成立的充要条件.

In this paper,we investigate the reverse order laws for { 1,2,3}-inverse of two-operator product by making full use of block-operator matrix technique. When A,B,AB are closed range operators,the equivalent conditions for B { 1,2,3 } A { 1,2,3 } =AB{ 1,2,3} and B{ 1,2,4} A{ 1,2,4} = AB{ 1,2,4} are presented.