算子的积分表示与范数在端点集上的可达性

Integral Representation of Operators and the Obtainability of Norm on the Extreme Points Set

给出了紧凸集上的连续的仿射算子或线性算子的积分表示定理，并证明了连续仿射算子的范数在紧凸集的端点集上可达．从而推广了Choquet定理并加深了对端点集的边界特性的刻画．

The paper establishes an integral representation theorem about the continuous affine or linear operators on a compact convex set, and proves that nouns of continuous affine operators are obtainable on the extreme points set of a compact convex set. Therefore, it extends Choquet's theorem and gets a deeper characterization of a boundary property for the extreme points sets.