Abstract

In this article we calculate the order projection in a space \(\mathcal{OA}_{r}(E,F)\) of all regular orthogonally additive operators from a vector lattice \(E\) to a Dedekind complete vector lattice \(F\), onto the band \(\{T\}^{\perp\perp}\) of \(\mathcal{OA}_{r}(E,F)\) which is generated by a disjointness preserving orthogonally additive operator \(T\colon E\to F\).

中文翻译：

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关于由不相交保持正交可加算子生成的带

摘要

在这篇文章中，我们计算所有正则正交加法算子在空间\(\mathcal{OA}_{r}(E,F)\)中从向量格\(E\)到戴德金完全向量格的阶次投影\(F\)，到由不相交产生的\(\mathcal{OA}_{r}(E,F)\)的带\(\{T\}^{\perp\perp}\)上保留正交加法运算符\(T\colon E\to F\)。