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

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.