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arXiv · 2402.10112

Amenable group actions on $L_p$ lattices

Antonio M. Scielzo
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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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Antonio M. Scielzo. 2024-02-15. Amenable group actions on $L_p$ lattices. https://arxiv.org/abs/2402.10112

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