Amenable group actions on L_p lattices

2024/02/15 by Scielzo, Antonio M. · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · doi:10.48550/arxiv.2402.10112

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 L_p lattice admits a model companion, which is stable and has quantifier elimination.

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• Invariant strictly convex renormings

Related

• Amenable partial actions
• Applications of orbit equivalence to actions of discrete amenable groups
• Banach L^p lattices with an automorphism
• Residuality of Dynamical Morphisms for Amenable Group Actions
• Minimal models for actions of amenable groups