This is an announcement for the paper "Compact groups of positive operators on Banach lattices" by Marcel de Jeu and Marten Wortel.
Abstract: In this paper we study groups of positive operators on Banach lattices. If a certain factorization property, for which we are not aware of counterexamples, holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is compact in the strong operator topology, it equals a group of isometric positive operators conjugated by a single central lattice automorphism, provided an additional technical assumption is satisfied, for which we again have only examples. We obtain a characterization of positive representations of a group with compact image in the strong operator topology, and use this for normalized symmetric Banach sequence spaces to prove an ordered version of the decomposition theorem for unitary representations of compact groups. Applications concerning spaces of continuous functions are also considered.
Archive classification: math.FA math.RT
Mathematics Subject Classification: Primary 22D12, Secondary 22C05, 46B42
Remarks: 21 pages
Submitted from: marten.wortel@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.1611
or