Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418611 | Journal of Mathematical Analysis and Applications | 2014 | 7 Pages |
Abstract
We introduce and study the class of almost limited sets in Banach lattices, that is, sets on which every disjoint weakâ null sequence of functionals converges uniformly to zero. It is established that a Banach lattice has order continuous norm if and only if almost limited sets and L-weakly compact sets coincide. In particular, in terms of almost Dunford-Pettis operators into c0, we give an operator characterization of those Ï-Dedekind complete Banach lattices whose relatively weakly compact sets are almost limited, that is, for a Ï-Dedekind Banach lattice E, every relatively weakly compact set in E is almost limited if and only if every continuous linear operator T:Eâc0 is an almost Dunford-Pettis operator.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jin Xi Chen, Zi Li Chen, Guo Xing Ji,