Weak compactness in the order dual of a vector lattice
Weak compactness in the order dual of a vector lattice
复制标题
DOI：
10.1090/s0002-9947-1974-0394098-6
复制
发表时间：
1974
影响因子：
1.3
通讯作者：
O. Burkinshaw
中科院分区：
文献类型：
--
作者：
O. Burkinshaw
如果E中存在x，使得对于所有n，Sk-l x < x，则向量格E中的序列x nI将被称为1 '序列。用Eb表示E的阶对偶。对于集合A C Eb，设1| IIAO表示E上的Minkowski泛函，由其在E中的极AO定义.一个集合A C Eb称为E上的等l '-连续的，如果lim|在E.本文的主要目的是用E和Eb上的序结构来刻画Eb中的紧性。特别地，研究了等l '-连续性与紧性的关系。? 2推广了Kaplan [81]关于Ec中Vague紧性的结果。然后用它来研究E中序列的Vague收敛性
A sequence x nI in a vector lattice E will be called an 1'sequence if there exists an x in E such that Sk-l x < x for all n. Denote the order dual of E by Eb. For a set A C Eb, let 1| IIAO denote the Minkowski functional on E defined by its polar AO in E. A set A C Eb will be called equi-l'-continuous on E if lim |IxnIIAO 0 for each 1t sequence lxn7 in E. Ihe main objective of this paper will be to characterize compactness in Eb in terms of the order structure on E and Eb. In particular, the relationship of equi-l'-continuity to compactness is studied. ?2 extends to Eac the results in Kaplan [81 on vague compactness in Ec. Then this is used to study vague convergence of sequences in E