论文标题
Banach Lattices上的无界Banach-Saks操作员和无界的Grothendieck操作员
Unbounded Banach-Saks operators and unbounded Grothendieck operators on Banach lattices
论文作者
论文摘要
假设$ e $是Banach晶格。最近，从订单的角度来看，关于已知的Banach-saks财产和Grothendieck财产的有激励性背景。在本文中，我们为享受Banach-Saks物业以及与Grothendieck物业相关的不同类型的运营商建立了这些结果。特别是，除了其他结果外，我们还表征了Banach Lattices的顺序连续性和反射性，该效率是根据其定义的相应有限运算符的角度来表征的。
Suppose $E$ is a Banach lattice. Recently, there have been some motivating contexts regarding the known Banach-Saks property and the Grothendieck property from an order point of view. In this paper, we establish these results for operators that enjoy different types considered for the Banach-Saks property as well as for different notions related to the Grothendieck property. In particular, beside other results, we characterize order continuity and reflexivity of Banach lattices in terms of the corresponding bounded operators defined on them.
