局部凸空间有限严格凸性和有限光滑性

Finite Strict Convexity and Finite Smoothness in Locally Convex Spaces

引入局部凸空间有限严格凸和有限光滑性的概念,建立对偶关系,证明局部凸空间中(XY)1的有限严格凸和有限光滑性既是Banach空间有限严格凸和有限光滑性概念在局部凸空间中的推广,又是局部凸空间k-严格凸和k-光滑性的自然推广.

The concept of finite strict convexity and finite smoothness space is introduced into locally convex space.It is shown that there exists a duality between finite strict convexity and finite smoothness,and some geometrical properties of quotient,finite strict convexity with（XY）1 and finite smoothness with（XY）1 are investigated in this thesis.