Let A be a uniformly complete vector lattice, let H be the collection of all order boundedlinear 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 therange of any orthomorphism π : A → A is an order ideal of A.
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机译：设A为一致完全的矢量格，设H为所有阶有界线性映射T的集合：A→R，使得| T（x）| = | T（| x |）|对于所有x∈A并令σ（A，H）为A上的弱拓扑。如果（A，σ（A，H））是一个完整的拓扑向量空间，则任何同胚性π的范围：A→A为阶理想的A。
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