正交及等距反射向量在lp空间的应用

doi:10.12677/AAM.2020.911217

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正交及等距反射向量在lp空间的应用
Application of Orthogonal and Isometric Reflection Vectors in lp Space

DOI: 10.12677/AAM.2020.911217, PDF,
作者: 吴思远^*, 计东海：哈尔滨理工大学理学院，黑龙江哈尔滨
关键词: Birkhoff正交；等腰正交的超平面；Roberts正交；正交基；线性赋范空间；Birkhoff Orthogonality； Isosceles Orthogonal Hyperplane； Roberts Orthogonality； Orthonormal Basis； Normed Linear Space

摘要: 在本文中，我们首先考虑有限维赋范线性空间中的正交基在l_p空间与Birkhoff正交的相关联系，其次考虑等距反射向量和L₂被加项向量在具体的lp空间中的联系以及当扩展到Hilbert空间中的一些性质变化。

Abstract: In this paper, we first consider the relationship between the orthogonal basis in the finite-dimensional normed linear space and the Birkhoff orthogonality in the l_p space, and then consider the relationship between the isometric reflection vector and L₂-summand vectors in the specific l_p space and some property changes when it is extended to Hilbert space.

文章引用：吴思远, 计东海. 正交及等距反射向量在lp空间的应用[J]. 应用数学进展, 2020, 9(11): 1887-1892. https://doi.org/10.12677/AAM.2020.911217

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