算子方程X^-1-A^*X^tA=Q的正算子解问题

The Positive Operator Solutions to Operator Equation X^-1-A^*X^tA=Q

在无限维可分Hilbert空间上研究了非线性算子方程X^-1-A^*X^tA=Q(t>1)的正算子解问题.利用算子论的知识,给出了该算子方程正算子解的特征以及正算子解存在的一些条件.在A为正规算子时,通过构造迭代系列的方法得到了该方程有正算子解的充分条件.

The positive solution of the nonlinear operator equation X^-1-A^*X^tA=Q(t>1)is studied in infinite dimensional separable Hilbert space.Using the knowledge of operator theory,the characteristics of the operator solutions of this equation and some conditions for the existence of the positive operator solutions are given.The sufficient conditions for the equation to have a operator solutions are obtained by constructing the iterative series method when A is a normal operator.