Compact groups of positive operators on Banach lattices

Details Compact groups of positive operators on Banach lattices Compact groups of positive operators on Banach lattices

2011-12-07

arxiv.org/abs/1112.1611v2

Mathematics

Functional Analysis

21 pages. Added a counterexample and fixed some typos, mathematical content is mostly unchanged

Scientific paper

In this paper we study groups of positive operators on Banach lattices. If a certain factorization property 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.

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