算子方程AX-XA*=B的正解与实正解

Positive and real-positive solutions of the operator equation AX-XA*=B

利用算子矩阵分块技巧和算子的广义逆,在A是幂等算子的情况下,给出了算子方程AX-XA*=B有正解和有实正解的充要条件,并给出了正解和实正解的通式。

Using the block operator matrix technique and generalized inverse of operator,when A is an idempotent,the suffcient and necessary conditions for the existence of positive solutions and real-positive solutions of the equation AX-XA＊= B and the representations of those solutions are established.