论文标题
Banach Lattices中无界绝对弱收敛上的某些特性
Some properties on the unbounded absolute weak convergence in Banach lattices
论文作者
论文摘要
在本文中，我们对$ uaw $ -convergence（分别$ $ convergence）与弱收敛之间的关系进行了更多研究。更确切地说，我们表征了Banach Lattices，每个弱的空序列都是$ uaw $ -Null。同样，我们表征了连续的Banach晶格，每个规范限制了$ un $ null Net（分别序列）弱均值弱。结果，我们研究了依次的$ uaw $ compact操作员与弱紧凑的操作员之间的关系。同样，事实证明，从Banach Lattice $ e $到非零Banach Space $ x $的每个连续运算符，并且仅当$ e^{\ prime} $是连续订单时，都是无限的。最后，我们使用$ uaw $ -Convergence序列给出了$ b $ weakly紧凑型操作员的新表征。
In this paper, we investigate more about relationship between $uaw$ -convergence (resp. $un$-convergence) and the weak convergence. More precisely, we characterize Banach lattices on which every weak null sequence is $uaw$-null. Also, we characterize order continuous Banach lattices under which every norm bounded $un$-null net (resp. sequence) is weakly null. As a consequence, we study relationship between sequentially $uaw$-compact operators and weakly compact operators. Also, it is proved that every continuous operator, from a Banach lattice $E$ into a non-zero Banach space $X$, is unbounded continuous if and only if $E^{\prime }$ is order continuous. Finally, we give a new characterization of $b$-weakly compact operators using the $uaw$-convergence sequences.
