Almost all positive continuous linear functionals can be extended
J. van Dobben de Bruyn (TU Delft - Discrete Mathematics and Optimization)
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Abstract
Let F be an ordered topological vector space (over R) whose positive cone F+ is weakly closed, and let E⊆ 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.
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