Almost all positive continuous linear functionals can be extended

Abstract Let F be an ordered topological vector space (over $$\mathbb {R}$$ R ) whose positive cone $$F_+$$ F + is weakly closed, and let $$E \subseteq F$$ E ⊆ a subspace. We prove that the set of continuous linear functionals on E can extended (positively continuously) to weak- $$*$$ ∗ dense in dual wedge $$E_+'$$ ′ . Furthermore, we show this result cannot generalized arbitrary operators, even finite-dimensional spaces.