| 摘要: |
| 设H和K为两个Hilbert空间，A∈B（H）和B∈B（K，H）满足ind（A）≤ 1，R（AB）⊆R（B），以及R（B）为闭.给出了等式R（AB）=R（A）∩R（B）成立的一个充分条件，并给出了上述等式不成立的一个反例. |
| 关键词: 算子值域 Drazin逆 Moore-Penrose逆 |
| DOI：10.3969/J.ISSN.1000-5137.2019.05.001 |
| 分类号:O177.1 |
| 基金项目:国家自然科学基金（11671261，11971136）；上海市科学技术委员会"一带一路"青年科学家基金（18590745200） |
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| A note on the range of the product of two operators |
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QIN Mengjie, XU Qingxiang
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| Let H and K be two Hilbert spaces,and let A∈B(H),B∈B(K,H) be two bounded linear operators such that ind(A) ≤ 1,R(AB)⊆R(B) and R(B) is closed in H.A sufficient condition is given under which R(AB)=R(A)∩R(B).Furthermore,a counterexample is constructed such that R(AB)≠R(A)∩R(B). |
| Key words: the range of an operator Drazin inverse Moore-Penrose inverse |
