论文标题
关于Riesz空间上的正交添加剂的一些评论
Some remarks on orthogonally additive operators on Riesz spaces
论文作者
论文摘要
我们研究了Riesz空间之间的正交加性操作员，而没有对范围空间的Dedekind完整性假设。我们的第一个结果给出了一对Riesz Spaces $（E，F）$的必要条件，每个正交添加剂从$ e $到$ f $均以横向订购的边界。第二个结果为具有$ s \ vee t $的一对正交添加剂$ s $和$ t $提供了足够的条件，并具有$ s \ wedge t $，因此，对于具有$ t^+$，$ t^+$，$ t^ - $或$ t^ - $ t^ - $ t^ - $ t^ - $ | t | $ noshing domain and domains space的正交操作符$ t $。最终，我们证明了迈耶定理的类似物，即为正交附加操作员设置的脱节模块保存操作员的存在。
We study orthogonally additive operators between Riesz spaces without the Dedekind completeness assumption on the range space. Our first result gives necessary and sufficient conditions on a pair of Riesz spaces $(E,F)$ for which every orthogonally additive operator from $E$ to $F$ is laterally-to-order bounded. Second result provides sufficient conditions on a pair of orthogonally additive operators $S$ and $T$ to have $S \vee T$, as well as to have $S \wedge T$, and consequently, for an orthogonally additive operator $T$ to have $T^+$, $T^-$ or $|T|$ without any assumption on the domain and range spaces. Finally we prove an analogue of Meyer's theorem on the existence of modules of disjointness preserving operator for the setting of orthogonally additive operators.
