| 算子方程X+A*X-tA=I的正算子解 |
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| 引用本文： | 张慧,郑小红,王立娟. 算子方程X+A*X-tA=I的正算子解[J]. 嘉兴学院学报, 2006, 18(3): 54-57 |
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| 作者姓名： | 张慧 郑小红 王立娟 |
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| 作者单位： | 嘉兴学院数学与信息科学学院,浙江嘉兴,314001 |
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| 摘 要： | 该文讨论了算子方程X＋A^＊X^-tA=I（t≥1）的正算子解，给出了方程正算子解存在的充要条件以及利用迭代的方法证明了方程极大解和极小解的存在。
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| 关 键 词： | 算子方程 正算子解 谱 |
| 文章编号： | 1008-6781（2006）03-0054-04 |
| 收稿时间： | 2005-09-08 |
| 修稿时间： | 2005-09-08 |
On the Positive Solutions of the Operator Equations X+A*X-tA=I |
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| ZHANG Hui,ZHENG Xiao-hong,WANG Li-juan. On the Positive Solutions of the Operator Equations X+A*X-tA=I[J]. Journal of Jiaxing College, 2006, 18(3): 54-57 |
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| Authors: | ZHANG Hui ZHENG Xiao-hong WANG Li-juan |
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| Affiliation: | College of Mathematics and Information Science, Jiaxing University, Jiaxing, Zhejiang 314001 |
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| Abstract: | In this note, we discuss positive solutions of the operator equation X+A~*X~(-t)A=I(t(?)1) in an infinite dimensional Hilbert space. Necessary and sufficient conditions for the existence of positive solution X of the operator equation have been obtained. We prove the existence of the maximum and minimum solutions of the operator equation. |
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| Keywords: | Operator equation Positive solution Spectrum. |
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