毕达哥拉斯正交与内积空间的一个特征性质

Characterizations of Inner Product Spaces and Pythagorean Orthogonality

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.

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.