This is an announcement for the paper "Persistence of Banach lattices under nonlinear order isomorphisms" by Denny H. Leung and Wee-Kee Tang.

Abstract: 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 c_0, and for Banach lattices that contain a closed sublattice order isomorphic to c_0.

Archive classification: math.FA

Mathematics Subject Classification: 46B42

Submitted from: weekeetang@ntu.edu.sg

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1507.02759

or

http://arXiv.org/abs/1507.02759