论文标题
Banach Lattices中的无界连续操作员和无限的Banach-Saks物业
Unbounded continuous operators and unbounded Banach-Saks property in Banach lattices
论文作者
论文摘要
在Banach空间之间的连续操作员的等效定义以虚弱的无效网络为动机，我们通过在Banach Lattices之间的连续操作员的定义中替换了无界的融合（$ uaw $ -convergence），从而引入了无限的连续操作员。我们表征了连续的Banach晶格和反射性Banach Lattices，以这些操作员的空间。此外，以无限弱的Cauchy序列来表征反身Banach晶格的动机，我们考虑在Banach Lattices之间进行预算的操作员，这些banach lattices将$ uaw $ uaw $ -cauchy序列映射到弱（$ uaw $ - $ uaw $ - 或norm norm）融合序列。这也使我们可以根据这些操作员来表征$ kb $ - 空格和反身空间。此外，我们将无限的Banach-Saks物业视为弱Banach-Saks物业的无限版本。拥有无限的Banach-saks财产之间存在许多相当大的关系，其空间由不同类型的Banach-saks财产满足。特别是，我们也以这些关系的方式表征了连续的Banach晶格。
Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce unbounded continuous operators by replacing weak convergence with the unbounded absolutely weak convergence ( $uaw$-convergence) in the definition of a continuous operator between Banach lattices. We characterize order continuous Banach lattices and reflexive Banach lattices in terms of these spaces of operators. Moreover, motivated by characterizing of a reflexive Banach lattice in terms of unbounded absolutely weakly Cauchy sequences, we consider pre-unbounded operators between Banach lattices which maps $uaw$-Cauchy sequences to weakly ( $uaw$- or norm) convergent sequences. This allows us to characterize $KB$-spaces and reflexive spaces in terms of these operators, too. Furthermore, we consider the unbounded Banach-Saks property as an unbounded version of the weak Banach-Saks property. There are many considerable relations between spaces possessing the unbounded Banach-Saks property with spaces fulfilled by different types of the known Banach-Saks property. In particular, we characterize order continuous Banach lattices in terms of these relations, as well.
