Amenable group actions on $L_p$ lattices
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916126760370176 |
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| author | Scielzo, Antonio M. |
| author_facet | Scielzo, Antonio M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Amenable group actions on $L_p$ lattices Scielzo, Antonio M. Dynamical Systems Functional Analysis Logic 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. |
| title | Amenable group actions on $L_p$ lattices |
| topic | Dynamical Systems Functional Analysis Logic |
| url | https://arxiv.org/abs/2402.10112 |