算子方程AX=C的正解问题

Positive Solutions of Operator Equation AX=C

利用Hilbert空间中有界线性算子的分块矩阵技巧,结合缺项算子矩阵的可补性和算子A的Moore-Penrose广义逆,得到了算子方程AX=C有自伴和正解的充要条件,并利用A的Moore-Penrose广义逆给出了通解.

Using the technique of block-operator matrices of bounded linear operators on a Hilbert space, the properties of operator matrices and the Moore-Penrose inverse of A, the sufficient and efficient conditions is obtained in which the operator equation AX = C has self-adjoint and positive solutions. Finally, the generalized self-adjoint and positive solutions of AX = C are given.