算子方程AXB=C的解

J4 ›› 2010, Vol. 45 ›› Issue (6): 74-80.

算子方程AXB=C的解

田学刚, 王少英

滨州学院数学与信息科学系, 山东滨州 256603

收稿日期:2009-11-27 出版日期:2010-06-16 发布日期:2010-06-17
作者简介:田学刚（1980-）,男,硕士,助教,研究方向为算子理论与小波分析. Email: xuegangtian@163.com
基金资助:
滨州学院青年基金资助项目(BZXYKJ0815)

Solutions to the operator equation AXB=C

TIAN Xue-gang, WANG Shao-ying

Department of Mathematics and Information Science, Binzhou University, Binzhou 256603, Shandong, China

Received:2009-11-27 Online:2010-06-16 Published:2010-06-17

摘要/Abstract

摘要：

利用算子矩阵分块技巧和算子广义逆,研究无限维Hilbert 空间上算子方程AXB=C的解,给出了该方程有解的充要条件和解的一般形式。特别地, 在B的值域包含A*的值域或A*的值域包含B的值域的情况下,得到了算子方程AXB=C有正解的充分必要条件, 并给出了正解的一般形式。

关键词: 算子方程;正算子;Moore-Penrose 逆

Abstract:

Using the block operator matrix technique and the generalized inverse of operator,the solutions to the operator equation AXB=C are studied in infinite Hilbert space. The sufficient and necessary condition for the existence of solutions to the equation AXB=C and the representation of the solutions are established. Especially when R(A*)R(B) or R(B)R(A*), the sufficient and necessary condition for the existence of positive solutions of the equation AXB=C and the general form of the positive solutions are also derived.

Key words: operator equation; positive operator; Moore-Penrose inverse

田学刚, 王少英. 算子方程AXB=C的解[J]. J4, 2010, 45(6): 74-80.

TIAN Xue-gang, WANG Shao-ying. Solutions to the operator equation AXB=C[J]. J4, 2010, 45(6): 74-80.

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