算子方程X^s+A~*X^(-t)A=I的正算子解

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

在无限维Hilbert空间上研究了算子方程Xs+A*X-tA=I(s≥1,t≥1)的正算子解问题,给出了算子方程Xs+A-X-tA=I的正算子解存在的一些必要条件.

Researched the positive operator solutions of the operator equationXs＋A＊X-tA=I（s≥1,t ≥ 1） in infinite Hilbert space.Some necessary conditions for the existence of positive operator solutions to this operator equation was established.