毕达哥拉斯正交与内积空间的一个特征性质  

Pythagorean orthogonality and characterization of inner product spaces

作　　者：孙公雨[1] 郭伟[1] 计东海[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,哈尔滨150080

出　　处：《哈尔滨商业大学学报（自然科学版）》2013年第1期122-124,共3页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(11171082);哈尔滨理工大学优博优硕培育计划资助项目(HLGYCX2011-022)

摘　　要：为研究毕达哥拉斯正交与内积空间之间的关系,证明了满足蕴含关系x,y∈Sx,x⊥Iy■‖x+y‖=2且维数不小于3的实赋范线性空间是内积空间,从而证明一个维数不小于3且满足蕴含关系x,y∈Sx,x⊥py■x⊥p(-y)的赋范线性空间X是一个内积空间.This paper explored the relationship between Pythagorean orthogonality and inner product spaces. It was proved that a real normed linear space, whose dimension was at least 3, satisfied the implication： x,y∈S;x⊥ry→｜｜x＋y｜｜=√2 was an inner product space. As a corollary, it was shown that a normed linear space whose dimension was at least 3 and satisfied the implication x,y∈Sx,x⊥py→x⊥p（-y）, was an inner product space.

关 键 词：内积空间 等腰正交 赋范线性空间 毕达哥拉斯正交 

分 类 号：O177[理学—数学]