关于Hausdorff拓扑向量空间中的nuclear锥的注记(英文)

A note on nuclear cone in Hausdorff topological vector space

考虑Hausdorff拓扑向量空间中一类重要的凸锥(即nuclear锥),给出了关于它的几个等价性质.特别的,证明了在Hausdorff拓扑向量空间中,nuclear锥与伪nuclear锥是等价的.作为应用,给出了Hausdorff拓扑向量空间中关于nuclear锥的有效点的存在结果,对原有的局部凸空间中的相应结果做了一个推广.

A kind of important convex cone (i.e., nuclear cone) in Hausdorff topological vector space is considered. Several equivalent characteristics of the nuclear cone are given. In particular, it is shown that the equivalence of the nuclear cone and the pseudonuclear cone in Hausdorff topological vector space. As an application, an existence result of efficient point for the nuclear cone in Hausdorff topological vector space is investigated, which is a generalization of the result in locally convex space.