Amenable group actions on $L_p$ lattices
Dynamical Systems
2024-02-16 v1 Functional Analysis
Logic
Abstract
A result by Ornstein and Weiss states that a free and measure-preserving action of an amenable group on a probability space yields a decomposition of the space in disjoint images, up to a small error, analogous to the one given by the Rokhlin lemma in the case of a single transformation. We generalise this result to non-singular actions, and use it to prove that the theory of an action by automorphisms of an amenable group on a Banach lattice admits a model companion, which is stable and has quantifier elimination.
Cite
@article{arxiv.2402.10112,
title = {Amenable group actions on $L_p$ lattices},
author = {Antonio M. Scielzo},
journal= {arXiv preprint arXiv:2402.10112},
year = {2024}
}