| 算子乘积的Moore-Penrose逆序律 |
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| 引用本文： | 张海燕.算子乘积的Moore-Penrose逆序律[J].数学的实践与认识,2014(11). |
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| 作者姓名： | 张海燕 |
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| 作者单位： | 商丘师范学院数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金天元基金(11326105);河南省教育厅科学技术研究重点项目(14B110010);河南省自然科学基金(122300410420) |
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| 摘 要： | 借助特殊的空间分解,重新刻画算子乘积的Moore-Penrose逆序律成立的充要条件.给出当A,B,AB为闭值域算子时,两个算子乘积Moore-Penrose逆序律成立当且仅当R(A*AB)=R(B)∩R(A*)=R(BB*A*).
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| 关 键 词： | Moore-Penrose逆 逆序律 分块算子矩阵 |
New Results of Reverse Order Law for Moore-Penrose Reverse |
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| Abstract: | In this paper,the reverse order law for Moore-Penrose reverse of a two-operator product is mainly investigated by making full use of block-operator matrix technique.When all ranges R(A),R(B) and R(AB) are closed,it is given that the reverse order law for MoorePenrose reverse holds if and only if R(A~* AB) = R(B) ∩ R(A~*) = R(BB~*A~*). |
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| Keywords: | reverse order law moore-penrose reverse block-operator matrix |
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