无限维Hilbert空间中算子方程的正算子解  

The Positive Operator Solutions of the Operator Equation in the Infinite Dimensional Hilbert Space

作　　者：赵转萍 ZHAO Zhuanping(Shanxi Vocational University of Engineering Science and Technology,Taiyuan 030619,China)

机构地区：[1]山西工程科技职业大学,山西太原030619

出　　处：《太原师范学院学报（自然科学版）》2021年第2期10-12,共3页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：在无限维Hilbert空间中利用算子理论基本知识,讨论一类算子方程X^(-s)+A^(*)X^(t)A=B(s≥1,0<t<1)正算子解的问题,给出算子方程正算子解的变化范围以及存在正算子解的条件,并通过构造算子序列给出算子方程存在正算子解的一个充分必要条件.Combining the operator theory,the positive operator solutions of the operator Equation X^(-s)+A^(*)X^(t)A=B are considered in the infinite dimensional Hilbert space.In this paper,we give the conditions for the existence of the positive operator solutions and the range of the solutions.Also,the necessary and sufficient conditions for the positive operator solutions are obtained by constructing the sequence of operators.

关 键 词：算子方程 正算子解 算子序列 

分 类 号：O177.1[理学—数学]