Abstract

We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identities of Kusraeva involving the root mean power and the geometric mean. Furthermore, it is shown that a polynomial on a vector lattice is orthogonally additive whenever it is orthogonally additive on the positive cone. These results improve recent characterizations of bounded orthogonally additive polynomials by G. Buskes and the author.

中文翻译：

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关于正交加性多项式的一些注意事项

摘要

我们分别使用 Kusraeva 的两个多项式恒等式涉及均方根和几何平均数，提供从一致完整向量格到凸出生学空间的有界正交加性多项式的两个新特征。此外，还表明只要向量格上的多项式在正锥体上正交相加，它就是正交相加的。这些结果改进了 G. Buskes 和作者最近对有界正交加性多项式的表征。