赋范空间中的角分线与内积空间的特征性质

Angular bisectors in normed linear spaces and a characterization of inner product spaces

为说明不同的角分线概念之间的关系对空间性质的影响,通过讨论D-角分线与G-角分线之间的关系,利用赋范线性空间中Birkhoff正交和等腰保持一致的充要条件,证明一个赋范线性空间中的D-角分线与G-角分线保持一致当且仅当该空间是内积空间。

To order to clarify how the difference between two different angular bisector types reflects the property of the underlying space,the relation between D-angular bisector and G-angular bisector is discussed.By using the necessary and sufficient condition for Birkhoff orthogonality and isosceles orthogonality to coincide in normed linear spaces,it is proved that D-angular bisector and G-angular bisector coincide if and only if the underlying normed linear space is an inner product space.