| 两子空间的公共补与Groβ问题 |
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| 引用本文： | 邓春源,杜鸿科.两子空间的公共补与Groβ问题[J].数学学报,2006,49(5):1099-111. |
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| 作者姓名： | 邓春源 杜鸿科 |
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| 作者单位： | 陕西师范大学数学科学学院,西安710062 |
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| 基金项目： | 国家自然科学基金资助项目（10571113） |
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| 摘 要： | 设U,V是Hilbert空间H的两个闭子空间．若存在H的闭子空间L满足L+U=H,L+V=H,且L∩U=L∩V={0},则称L是U和V的公共补．本文获得了两子空间有公共补的一些新的特征,给出了等式H=U∩(U⊥+ V⊥)]⊕V⊕(U⊥∩V⊥)]成立的充分必要条件,完全回答了GroB提出的问题．
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| 关 键 词： | 谱 投影 投影对 |
| 文章编号： | 0583-1431（2006）05-1099-14 |
| 收稿时间： | 2005-05-16 |
| 修稿时间： | 2005-05-162005-07-30 |
Common Complements of Two Subspaces and an Answer to GroB's Question |
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| Chun Yuan DENG ,Hong Ke DU.Common Complements of Two Subspaces and an Answer to GroB''s Question[J].Acta Mathematica Sinica,2006,49(5):1099-111. |
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| Authors: | Chun Yuan DENG Hong Ke DU |
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| Institution: | Chun Yuan DENG Hong Ke DU College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China |
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| Abstract: | Suppose that U and V are two subspaces of a Hilbert space H. If there exists a subspace L such that L+ U=H, L+V=H and L∩U=L∩V= {0}, then L is said to be a common complement of U and V. In this paper, some new characteristics of common complements of two subspaces are obtained. Meanwhile, a necessary and sufficient condition for the equation H=U∩(U⊥+ V⊥)]⊕V⊕(U⊥∩V⊥)] to hold is given, which it is a complete answer to GroB's question. |
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| Keywords: | spectrum projection pair of projections |
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