算子方程A*X+XA=B的解

Solutions of the Operator Equation A*X+XA=B

设A和B是复可分Hilbert空间H上两个有界线性算子,利用算子矩阵分块技巧和算子的广义逆,在A是幂等算子或广义幂等算子的情况下,给出了算子方程A*X+XA=B有解和有自伴解的充要条件,并给出了算子方程A*X+XA=B的解和自伴解的一般形式.

Let A,Bbe two bounded linear operators on a complex separable Hilbert space H.Using the block operator matrix technique and generalized inverse of operator,when Ais an idempotent or a generalized idempotent operator,the sufficient and necessary conditions for the existence of solutions and self-adjoint solutions of the equation A＊X＋XA=Band the representations of those solutions are established.