论文标题
紧凑型凸的中心
Centre of a compact convex set
论文作者
论文摘要
我们介绍了凸组集合的概念中心，并研究了带有中心的紧凑型凸面上连续仿射函数的空间。我们表明，这些空间恰恰是基本规范空间的双重二元空间，在该空间中，下面的基座具有（唯一）中心。我们还表征了相应的基本规范空间。我们在局部凸空间的紧凑，平衡，凸子集上获得条件，以便在凸集中连续仿射函数的相应空间是绝对阶的单位空间。同样，我们表征了基座上的条件，该状态具有基础规范空间的中心，以使后者成为绝对的基础规范空间。
We introduce the notion centre of a convex set and study the space of continuous affine functions on a compact convex set with a centre. We show that these spaces are precisely the dual of a base normed space in which the underlying base has a (unique) centre. We also characterize the corresponding base norm space. We obtain a condition on a compact, balanced, convex subset of a locally convex space so that the corresponding space of continuous affine functions on the convex set is an absolute order unit space. Similarly, we characterize a condition on the base with a centre of a base normed space so that the latter becomes an absolutely base normed space.
