Nearly approximate transitivity (AT) for circulant matrices
Dynamical Systems
2019-08-15 v1 Operator Algebras
Abstract
By previous work of Giordano and the author, ergodic actions of (and other discrete groups) are completely classified measure-theoretically by their dimension space, a construction analogous to the dimension group used in C*-algebras and topological dynamics. Here we investigate how far from AT (approximately transitive) can actions be which derive from circulant (and related) matrices. It turns out not very: although non-AT actions can arise from this method of construction, under very modest additional conditions, ATness arises; in addition, if we drop the positivity requirement in the isomorphism of dimension spaces, then all these ergodic actions satisfy an analogue of AT. Many examples are provided
Cite
@article{arxiv.1411.6301,
title = {Nearly approximate transitivity (AT) for circulant matrices},
author = {David Handelman},
journal= {arXiv preprint arXiv:1411.6301},
year = {2019}
}