| 缺项算子矩阵的逆补 |
| |
| 引用本文： | 任芳国,黄建科. 缺项算子矩阵的逆补[J]. 西北大学学报(自然科学版), 2006, 36(2): 173-175 |
| |
| 作者姓名： | 任芳国 黄建科 |
| |
| 作者单位： | 陕西师范大学数学与信息科学学院，西安陆军学院数学教研室 陕西 西安 710062，陕西 西安 710108 |
| |
| 基金项目： | 国家自然科学基金资助项目(10571114)，陕西师范大学重点基金资助项目(995281) |
| |
| 摘 要： | 目的给出算子逆配置及缺项算子矩阵的逆补刻画。方法利用空间分解、极分解及构造算子矩阵的技巧。结果对给定的算子A∈B(?),B∈B(?),得到存在算子F∈B(?), 使得算子A BF可逆的条件;特别对定义在(?)上的缺项算子矩阵{A? B?},刻画了存在算子对(X,Y),其中(X,Y)∈ B(?)×B(?),使得补矩阵MX,Y=(AX BY)可逆的条件。结论利用获得结果,可对算子逆配置问题作进一步的研究。
|
| 关 键 词： | 算子矩阵 算子补 逆补 广义逆算子 |
| 文章编号： | 1000-274X（2006）02-0173-03 |
| 收稿时间： | 2004-11-04 |
| 修稿时间： | 2004-11-04 |
On the invertible completions of operator partial matrices |
| |
| REN Fang-guo,HUANG Jian-ke. On the invertible completions of operator partial matrices[J]. Journal of Northwest University(Natural Science Edition), 2006, 36(2): 173-175 |
| |
| Authors: | REN Fang-guo HUANG Jian-ke |
| |
| Abstract: | Aim To characterize the invertible assignment problem and the invertible completion on operator pairs. Methods Using the space decomposition, the polar decomposition and the construction technique in operator matrix. Results Given operators A and B acting on complex Hilbert spaces (?) and (?), respectively, the conditions indicate that there exists an operator F such that A BF is invertible. Especially, for a partial operator matrix {A? B?} defined on (?), the sufficient conditions are gained to have a pair (X,Y) of operators such that MX,Y = (AX BY) is invertible. Conclusion By using the results obtained, the invertible completion can be further explored. |
| |
| Keywords: | operator matrix operator completion invertible completion generalized inverse operator |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
