Banach $L^p$ lattices with an automorphism

Antonio M. Scielzo

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arXiv · 2304.09798

Banach $L^p$ lattices with an automorphism

Antonio M. Scielzo

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Abstract

We study the theory of Banach $L^p$ lattices with a distinguished automorphism, in the framework of continuous logic. Using a functional version of the Rokhlin lemma, we prove that it admits a model companion, which is stable and has quantifier elimination. We show that the types of this theory that are not trivial cannot be isolated. We then use this result to obtain a proof of the absence of comeagre conjugacy classes in $\operatorname{Aut}^*({\mu})$, the Polish group of non-singular transformations of a standard probability space.

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BibTeX RIS

Antonio M. Scielzo. 2023-04-19. Banach $L^p$ lattices with an automorphism. https://arxiv.org/abs/2304.09798

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