Persistence of Banach lattices under nonlinear order isomorphisms |
| |
Authors: | Denny H Leung Wee-Kee Tang |
| |
Institution: | 1.Department of Mathematics,National University of Singapore,Singapore,Singapore;2.Division of Mathematical Sciences,Nanyang Technological University,Singapore,Singapore |
| |
Abstract: | Ordered vector spaces E and F are said to be order isomorphic if there is a (not necessarily linear) bijection \(T: E\rightarrow F\) such that \(x\ge y\) if and only if \(Tx \ge Ty\) for all \(x,y \in E\). We investigate some situations under which an order isomorphism between two Banach lattices implies the persistence of some linear lattice structure. For instance, it is shown that if a Banach lattice E is order isomorphic to C(K) for some compact Hausdorff space K, then E is (linearly) isomorphic to C(K) as a Banach lattice. Similar results hold for Banach lattices order isomorphic to \(c_{0}\), and for Banach lattices that contain a closed sublattice order isomorphic to \(c_{0}\). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|