| 毕达哥拉斯正交与内积空间的一个特征性质 |
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| 引用本文： | 姚君.毕达哥拉斯正交与内积空间的一个特征性质[J].北华大学学报(自然科学版),2011,12(4):406-407. |
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| 作者姓名： | 姚君 |
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| 作者单位： | 黑龙江科技学院理学院,黑龙江哈尔滨,150027 |
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| 摘 要： | 利用Singer正交的相关结论,证明了一个维数不小于3的赋范线性空间X是一个内积空间当且仅当X的单位球面上的任一点均存在一个过原点的超平面H使得X毕达哥拉斯正交于H.
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| 关 键 词： | 毕达哥拉斯正交 Singer正交 内积空间 特征性质 |
Characterizations of Inner Product Spaces and Pythagorean Orthogonality |
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| YAO Jun.Characterizations of Inner Product Spaces and Pythagorean Orthogonality[J].Journal of Beihua University(Natural Science),2011,12(4):406-407. |
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| Authors: | YAO Jun |
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| Institution: | YAO Jun(Heilongjiang Institute of Science and Technology,Harbin 150027,China) |
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| Abstract: | By using the related results of Singer orthogonality,it is proved that a normed linear space X with dimension not less than three is an inner product space if and only if for each vector X in the unit sphere,there exists a hyperplane H passing through the origin such that X is Pythagorean orthogonal to H. |
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| Keywords: | Pythagorean orthogonality Singer orthogonality inner product spaces Characterizations |
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