一类算子方程的正解

Positive Solutions to Some Operator Equation

设A,B,C是Hilbert空间H上三个有界线性算子.利用算子矩阵分块技巧,在B*的核空间包含A*的值域空间或A的核空间包含B的值域空间的情况下,研究了算子方程AXB=C有正解的充分必要条件,并给出了正解的一般形式.

Let A,B,C be three bounded linear operators on a Hilbert sqace . By using the block operator matrix,when the dernel sqace of B＊ includes the rance of A＊ or the kernel sqace of A includes the range sqace of B,the sufficient and necessary conditions for the existence of positive solutions of the operator equation AXB = C and the representation of the solutions are established.