| 算子方程x＋a^＊x^—1a=e的正定解 |
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| 引用本文： | 宁刚. 算子方程x＋a^＊x^—1a=e的正定解[J]. 襄樊学院学报, 2000, 21(2): 15-18 |
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| 作者姓名： | 宁刚 |
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| 作者单位： | 襄樊学院,数学系,湖北,襄樊,441053 |
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| 摘 要： | 本在Ｖｏｎ Ｎｅｕｍａｎｎ代数中引入了正定元的概念，给出了其判定定理和性质；研究了Ｖｏｎ Ｎｅｕｍａｎｎ代数中方程ｘ＋ａ＾＊ｘ＾－１ａ＝ｅ有正定解的必要条件和充分条件，构造了方程正定解的递归序列，并研究了其性质。
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| 关 键 词： | 正定元 正定解 算子方程 V－N代数 C^＊－代数 |
| 文章编号： | 1009-2854(2000)02-0015-04 |
| 修稿时间： | 2000-02-09 |
Positive Definite Solutions of Operator Equation x + a*x-1a = e |
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| NING Gang. Positive Definite Solutions of Operator Equation x + a*x-1a = e[J]. Journal of Xiangfan University, 2000, 21(2): 15-18 |
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| Authors: | NING Gang |
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| Abstract: | In this article, the concept of positive definite element in a von Neumann algebra is introduced,the character of positive definite element is given; the necessary conditions and sufficient conditions ofpositive definite solutions of equation x a *x-1a = e are studied, and the iterative sequence of positivedefinite solution of equation is set up, whose properties are also studied. |
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| Keywords: | Von Neumann algebra Positive element Positive definite element Strong convergence Positive definite solution |
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