算子方程X^s+A~*X^(-t)A=I的正算子解

On positive operator solutions of operator equation X^s+A~*X^(-t)A=I

结合算子理论的相关知识,将矩阵方程的某些结果推广到相应的算子方程上.讨论无限维Hilbert空间上算子方程Xs+A*X-tA=I(s>0,t>0)的正算子解及其解的范围.

Combining the operator theory, some results on matrix equation are extended to operator equation. In this paper, the operator equation X^s ＋A^＊ X^-tA = I （s〉0,t〉0） on the infinite dimensional Hilbert space is considered. The positive operator solutions of the equation are mainly discussed, and the location of the solutions is given.