赋范空间中广义角分线及其相关性质

Generalized angular bisectors and related properties in normed linear spaces

为说明不同角分线之间的关系对空间性质的影响,通过讨论B-角分线和D-角分线之间的关系证明若赋范线性空间中B-角分线与D-角分线保持一致,则该空间是欧氏空间.并且利用此结论得到了赋范空间成为欧氏空间的新的特征性质.

To illustrate how the different angular bisector types affect the properties of the un- derlying spaces, by discussing the relations between B - angular bisector and D - angular bi- sector, proved that the underlying normed linear space was a Euclidean space if B- angular bisector and D - angular bisector eoincide. Furthermore, new characterization properties are obtained to prove a normed linear Space was a Euclidean space.