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

作　　者：杨凯凡[1] YANG Kai-fan(School of Mathematical and Computer Science,Shaanxi University of Technology,Hanzhong 723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001

出　　处：《数学的实践与认识》2020年第18期206-208,共3页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301318);陕西省教育厅自然科学基金(18JK0162);陕西理工大学科研基金项目(SLG1910)。

摘　　要：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.

关 键 词：算子方程 正算子 正规算子 

分 类 号：O177[理学—数学]