严格端点与多面体形赋范空间

Strictly Extreme Points and Polyhedral Normed Spaces

本文研究了凸α-体的切锥,切流形及切空间与凸α-体的Minkowski泛函的次微分之间的关系.对于凸α-体的每个代数边界点,存在一个拟直和分解使按代数意义该边界点既是一个子空间的光滑点又是拟余子空间的严格端点.所获一般结论可有效地用于多面体形赋范空间理论.

The relationship between the tangent cone, the tangent manifold and the tangent space of a convex a-body and the subdifferential of the Minkowski functional of the convex α-body is investigated. For each algebraic boundary point of a convex α-body, there exists a quasi-direct sum decomposition such that in the algebraic sense the boundary point is both a subspace smooth point and a quasi-complementary subspace strictly extreme point. The general results obtained are efficiently applied to the theory of polyhedral normed spaces.