| 算子方程AXB=C的解 |
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| 引用本文： | 田学刚,王少英. 算子方程AXB=C的解[J]. 山东大学学报(理学版), 2010, 45(6): 74-80 |
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| 作者姓名： | 田学刚 王少英 |
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| 作者单位： | 滨州学院数学与信息科学系,山东滨州,256603 |
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| 基金项目： | 滨州学院青年基金资助项目 |
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| 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。
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| 关 键 词： | 算子方程 正算子 Moore-Penrose 逆 |
| 收稿时间： | 2009-11-27 |
Solutions to the operator equation AXB=C |
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| TIAN Xue-gang,WANG Shao-ying. Solutions to the operator equation AXB=C[J]. Journal of Shandong University, 2010, 45(6): 74-80 |
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| Authors: | TIAN Xue-gang WANG Shao-ying |
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| Affiliation: | Department of Mathematics and Information Science, Binzhou University, Binzhou 256603, Shandong, China |
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| 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. |
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| Keywords: | operator equation positive operator Moore-Penrose inverse |
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