算子方程X+A^(*)X^(-t) A=I的正算子解的刻画  

Characterization of positive operator solutions to operator equation X+A^(*)X^(-t)A=I

作　　者：杨凯凡[1] YANG Kai-fan(School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723000,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723000

出　　处：《陕西理工大学学报（自然科学版）》2021年第3期34-37,共4页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(11301318);陕西省教育厅自然科学基金资助项目(18JK0162);陕西理工大学科研计划项目(SLG1910)。

摘　　要：在无限维可分Hilbert空间上研究算子方程X+A^(*)X^(-t) A=I的正算子解的存在性问题。首先,给出了方程正算子解范数、谱半径的范围;其次,通过构造有效的迭代序列,给出算子方程X+A^(*)X^(-t) A=I有正算子解的一些条件。In this paper,the positive operator solutions to operator equation X+A^(*)X^(-t) A=I is studied in infinite dimensional Hilbert space.Firstly,the range of norm,the spectral radius of the solution to the equation are given.secondly,by constructing effective iterative sequence,it gives some conditions for the existence of positive operator solutions to operator equation X+A^(*)X^(-t) A=I.And finally,using space decomposition and operator block,the relationship of solutions to two kinds of equations is studied.

关 键 词：算子方程 可逆算子 谱分解 谱半径 

分 类 号：O177.91[理学—数学]