Nearly Approximate Transitivity (AT) for Circulant Matrices

被引：1

作者：

Handelman, David ^{[1
]}

机构：

[1] Univ Ottawa, Math Dept, Ottawa, ON K1N 6N5, Canada

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2019年 / 71卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

approximately transitive; ergodic transformation; circulant matrix; hemicirculant matrix; dimension space; matrix-valued random walk;

D O I：

10.4153/CJM-2017-041-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 approximately transitive (AT) actions can be that 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, approximate transitivity arises. KIn 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.

引用

页码：381 / 415

页数：35