【摘要】 为了研究Minkowski平面中的等幂性质能否决定空间的整体性质,利用几何方法,给出了非严格凸赋范平面单位圆内部等幂点可能的存在区域,依据范数传递性相关理论,证明了如果一个Minkowski平面的单位圆存在一个大点并且其内部存在一个非零等幂点,那么该空间是一个Hilbert空间.更多还原

【Abstract】 In order to study whether equipower property can decide the global property of a space,the possible region in which equipower points of the unit circle might exist is presented in a non-strictly convex normed plane via geometric method. By applying known results concerning transitivity of the norm,it is proved that if the unit circle of a Minkowski plane admits an equipower point other than the origin as well as a big point,then the space is a Hilbert space.更多还原