Furstenberg Transformations and Approximate Conjugacy

Details Furstenberg Transformations and Approximate Conjugacy Furstenberg Transformations and Approximate Conjugacy

2005-05-02

arxiv.org/abs/math/0505028v1

Mathematics

Operator Algebras

Scientific paper

Let $\alpha$ and $\beta$ be two Furstenberg transformations on 2-torus associated with irrational numbers $\theta_1,$ $\theta_2,$ integers $d_1, d_2$ and Lipschitz functions $f_1$ and $f_2.$ We show that $\alpha$ and $\beta$ are approximately conjugate in a measure theoretical sense if (and only if) $\bar{\theta_1\pm \theta_2}=0$ in $\R/\Z.$ Closely related to the classification of simple amenable $C^*$-algebras, we show that $\alpha$ and $\beta$ are approximately $K$-conjugate if (and only if) $\bar{\theta_1\pm \theta_2}=0$ in $\R/\Z$ and $|d_1|=|d_2|.$ This is also shown to be equivalent to that the associated crossed product $C^*$-algebras are isomorphic.

Affiliated with

Also associated with

No associations

Rating

Furstenberg Transformations and Approximate Conjugacy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Furstenberg Transformations and Approximate Conjugacy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Furstenberg Transformations and Approximate Conjugacy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-479756