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- SHIJIE LU
- DEPARTMENT OF MATHEMATICS ZHEJIANG UNIVERSITY HANGZHOU PEOPLE'S REPUBLIC OF CHINA
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By definition the cosine of the angle between the two subspaces M and N is { \left| {u, v} \ ight|:u \in M, v \in N, \left// u \ ight// = 1 = \left// v \ ight//} . For operators A and B with closed range in Hilbert spaces, AB has closed range if and only if the angle between ker A and B({(\ker AB)^ ⊥ }) is positive. Moreover, if we denote by {A^Ψ } the pseudo-inverse of A, then {(AB)^Ψ } = {B^Ψ }{A^Ψ } if and only if B({(\ker AB)^ ⊥ }) \subset {(\ker A)^ ⊥ } and {A^ * }({(\ker {B^ * }{A^ * })^ ⊥ }) \subset {(\ker {B^ * })^ ⊥ }.
収録刊行物
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- Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ
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Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ 39 (1), 89-94, 1987
東北大学大学院理学研究科数学専攻
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- CRID
- 1390282680091478912
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- NII論文ID
- 110000026408
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- NII書誌ID
- AA00863953
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- ISSN
- 2186585X
- 00408735
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- MRID
- 876455
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