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Nearly approximate transitivity (AT) for circulant matrices by Handelman, David is a scholarly article available to read on EtoBox.

What is Nearly approximate transitivity (AT) for circulant matrices about?

By previous work of Giordano and the author, ergodic actions of $\Z$ (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

Author

Handelman, David

Published

2014

Language

EN