| 关于$\{1,3,4\}$-逆的混合逆序律 |
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| 引用本文： | 张海燕,邓春源.关于$\{1,3,4\}$-逆的混合逆序律[J].数学研究及应用,2019,39(5):529-539. |
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| 作者姓名： | 张海燕 邓春源 |
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| 作者单位： | 商丘师范学院数学与统计学院, 河南 商丘 476000,华南师范大学数学科学学院, 广东 广州 510631 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11501345; 11671261), 河南省高等学校青年骨干教师资助计划(Grant No.2017GGJS140). |
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| 摘 要： | In this paper, we study the mixed-type reverse order laws to {1, 3, 4}-inverses for closed range operators A, B and AB. It is shown that B{1, 3, 4}A{1, 3, 4} ?(AB){1, 3} if and only if R(A*AB) ? R(B). For every A(134)∈ A{1, 3, 4}, it has(A(134)AB){1, 3, 4}A{1, 3, 4} =(AB){1, 3, 4} if and only if R(AA*AB) ? R(AB). As an application of our results, some new characterizations of the mixed-type reverse order laws associated to the Moore-Penrose inverse and the {1, 3, 4}-inverse are established.
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| 关 键 词： | $\{1 3 4\}$-逆 逆序律 广义逆 分块算子矩阵 |
| 收稿时间： | 2018/12/16 0:00:00 |
| 修稿时间： | 2019/5/26 0:00:00 |
Mixed-Type Reverse Order Laws Associated to $\{1,3,4\}$-Inverse |
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| Haiyan ZHANG and Chunyuan DENG.Mixed-Type Reverse Order Laws Associated to $\{1,3,4\}$-Inverse[J].Journal of Mathematical Research with Applications,2019,39(5):529-539. |
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| Authors: | Haiyan ZHANG and Chunyuan DENG |
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| Abstract: | In this paper, we study the mixed-type reverse order laws to $\{1,3,4\}$-inverses for closed range operators $A$, $B$ and $AB$. It is shown that $B\{1,3,4\}A\{1,3,4\}\subseteq (AB)\{1,3\}$ if and only if $R(A^*AB)\subseteq R(B)$. For every $A^{(134)}\in A\{1,3,4\}$, it has $(A^{(134)}AB)\{1,3,4\}A\{1,3,4\}= (AB)\{1,3,4\}$ if and only if $R(AA^*AB)\subseteq R(AB)$. As an application of our results, some new characterizations of the mixed-type reverse order laws associated to the Moore-Penrose inverse and the $\{1,3,4\}$-inverse are established. |
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| Keywords: | $\{1 3 4\}$-inverse reverse order law generalized inverse block-operator matrix |
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