| 赋范线性空间中的弧长正交 |
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| 引用本文： | 王麟,董新建. 赋范线性空间中的弧长正交[J]. 哈尔滨理工大学学报, 2014, 0(2): 106-110 |
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| 作者姓名： | 王麟 董新建 |
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| 作者单位： | [1]黑龙江科技大学理学院,黑龙江哈尔滨150022 [2]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080 |
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| 基金项目： | 国家自然科学基金（11001068,11171082,11371114）;黑龙江省教育厅科学技术研究项目（12523045,12521479）. |
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| 摘 要： | 研究了赋范线性空间中弧长正交的存在唯一性和正交对角线的存在唯一性.根据勾股正交的等腰正交(勾股正交)的齐次方向的相关结果,讨论了弧长正交和等腰正交(勾股正交)的关系,并证明在实Banach空间中,如果在给定的单位向量的某个邻域与单位球面的交集中等腰正交(或勾股正交)蕴含着弧长正交或者弧长正交蕴含着等腰正交(或勾股正交),则该Banach空间是一个内积空间.
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| 关 键 词： | 赋范线性空间 弧长正交 等腰正交 勾股正交 内积空间的特征性质 |
Arc-length Orthogonality in Normed Linear Spaces |
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| WANG Lin,DONG Xin-jian. Arc-length Orthogonality in Normed Linear Spaces[J]. Journal of Harbin University of Science and Technology, 2014, 0(2): 106-110 |
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| Authors: | WANG Lin DONG Xin-jian |
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| Affiliation: | (College of Science, Heilongjiang Institution of Science and Technology, Harbin 150022, China;School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China) |
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| Abstract: | The existence and uniqueness properties of arc-length orthogonality and the existence and uniqueness of orthogonal diagonals in the sense of arc-length orthogonality are studied in normed linear spaces.By applying related results of homogeneous direction of isosceles orthogonality （Pythagorean orthogonality,resp.）,the relation of arc-length orthogonality to isosceles orthogonality （Pythagorean orthogonality,resp） is studied.It is proved that if isosceles orthogonality （Pythagorean orthogonality,resp.） implies arc-length orthogonality or arc-length orthogonality implies isosceles orthogonality （Pythagorean orthogonality,resp.） in the intersection of a neighborhood of a fixed unit vector and the unit sphere in a real Banach space,then the underlying space is an inner product space. |
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| Keywords: | normed linear spaces arc-length orthogonality isosceles orthogonality Pythagorean orthogonality characterizations of inner-product spaces |
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