Banach空间的特征函数

Characteristic Function of Banach Space

通过一类特殊的单调算子(实Banach空间X范数的次微分算子),引入一类具有特殊性质的实变量的实值函数——X的特征函数。Banach空间X的许多几何性质,比如各种常规的凸性、光滑性,都可以用其特征函数相应的性质给于刻划。另外,利用特征函数给出了:①X是Hiebert空间的一个充要条件,从另一个角度刻划了Hiebert空间的特性;②X的凸性模、光滑模的等价条件。

A kind of characteristic function of Banach spaces having spacial properties is introduced by some monotone oprators Many geometric characterizations of Banach Spaces, such as various convexity and smoothness, can be represented by means of corresponding properties of these functions Moreover, a necessary and sufficient condition of which Banach Space Xis Hiebert space and some equivalent conditions with respect to X are given by the characteristic functions, and the characters of Hiebert space are depicted in the another aspect.