2015/07/10 by Denny H. Leung, Leung, Denny H., Wee-Kee Tang +1
Mathematics · #46B42 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B42
paper · pdf · doi:10.48550/arxiv.1507.02759
arxiv created 2015/07/10 · arxiv updated 2015/07/13
Ordered vector spaces E and F are said to be order isomorphic if there is a (not necessarily linear) bijection between them that preserves order. 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 c0, and for Banach lattices that contain a closed sublattice order isomorphic to c0.