| 两个算子乘积的{1,3,4}逆序律 |
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| 引用本文： | 段樱桃.两个算子乘积的{1,3,4}逆序律[J].山东大学学报(理学版),2012,47(4):53-56,61. |
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| 作者姓名： | 段樱桃 |
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| 作者单位： | 湛江师范学院数学与计算科学学院,广东湛江,524048 |
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| 基金项目： | 国家自然科学基金资助项目(10871224);湛江师范学院自然科学研究资助项目(QL1001) |
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| 摘 要： | 利用算子分块矩阵的技巧,研究了两个算子乘积的{1,3,4}逆的广义逆序律,证明了当R(A)、R(B)以及R(AB)都闭时,(AB){1,3,4}=B{1,3,4}.A{1,3,4}当且仅当R(B)=R(A*AB),或者R(A*)R(B)且B*(R(B)∩N(A))=B+(R(B)∩N(A))。
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| 关 键 词： | 广义逆 分块算子矩阵 逆序律 |
The reverse order law for {1,3,4}-inverse of the product of two operators |
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| DUAN Ying-tao.The reverse order law for {1,3,4}-inverse of the product of two operators[J].Journal of Shandong University,2012,47(4):53-56,61. |
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| Authors: | DUAN Ying-tao |
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| Institution: | DUAN Ying-tao(College of Mathematics and Computation Science,Zhanjiang Normal University,Zhanjiang 524048,Guangdong,China) |
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| Abstract: | The reverse order law for {1,3,4}-inverse of the product of two operators is investigated by using the technique of block-operator matrix and when R(A)、R(B)、R(AB) are closed.It is proved that(AB){1,3,4}=B{1,3,4}·A{1,3,4} if and only if R(B)=R(A*AB),or R(A*)R(B) and B*(R(B)∩N(A))=B+(R(B)∩N(A)). |
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| Keywords: | generalized inverse block-operator matrix reverse order law |
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