线性算子的实正与自伴广义逆

Re-nnd and hermitian generalized inverses of linear operators

设B(H)是复Hilbert空间H上有界线性算子全体组成的集合。设A、B∈B(H),通过探讨算子方程AX=B的实正解和自伴解存在的充要条件,研究闭值域算子的实正{1}-逆,{1,3}-逆,{1,4}-逆,{1,3,4}-逆存在的充要条件及其自伴{1,3}-逆,{1,4}-逆,{1,3,4}-逆存在的充要条件。

Let B（H） be the set of all bounded linear operators on the complex Hilbert space H.Let A,BE B（H）. By discussing some necessary and sufficient conditions for the existence of Re- nnd solution and hermitian solution of the operator equation AX= B, some necessary and sufficient conditions for the existence of Re-nnd { 1 }-, { 1,3 }-, { 1,4 }-, { 1,3,4 }-inverses and hermitian {1,3}-,{1,4}-, {1,3,4}-inverses for an operator with closed range are given.