对偶空间上凸函数的逼近

设Banach空间E具有等价二次严格凸范数, f为其对偶空间E^*上的w^*下半连续Lipschitz凸函数, 该文证明了E^*上存在w^*下半连续且很光滑点集稠密(从而在稠子集上Gateaux可微)的Lipschitz 凸函数的单调序列{f_n}在有界集上一致逼近f.

Approximation of Convex Functions on the Dual Spaces

In this paper, the authors prove that for every $w+*$ lower semicontinuous Lipschitzian convex function on the dual of a bistrictly convexifiable Banach space can be uniformly approximated by a sequence of $w+*$ lower semicontinuous monotone nondecreasing Lipschitzian convex function with the dense very smooth point set.