Abstract
Let A be a uniformly complete vector lattice, let H be the collection of all order bounded linear mappings T : A → ℝ such that |T(x)| = |T(|x|)| for all x ∈ A and let σ(A, H) the weak topology on A. If (A, σ(A, H)) is a complete topological vector space then the range of any orthomorphism π: A → A is an order ideal of A.
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