论文标题
几乎所有积极的连续线性函数都可以扩展
Almost all positive continuous linear functionals can be extended
论文作者
论文摘要
令$ f $为一个有序的拓扑矢量空间（超过$ \ m马布{r} $），其正锥$ f _+$是弱关闭的，让$ e \ e \ subseteq f $为子空间。我们证明，$ e $上的一组正连续线性功能集可以扩展（积极，连续）到$ f $很弱 - $*$ $*$密度在拓扑双wedge $ e _+'$中。此外，我们表明，即使在有限维空间中，也无法将此结果推广到任意正算子。
Let $F$ be an ordered topological vector space (over $\mathbb{R}$) whose positive cone $F_+$ is weakly closed, and let $E \subseteq F$ be a subspace. We prove that the set of positive continuous linear functionals on $E$ that can be extended (positively and continuously) to $F$ is weak-$*$ dense in the topological dual wedge $E_+'$. Furthermore, we show that this result cannot be generalized to arbitrary positive operators, even in finite-dimensional spaces.
