Vol. 71, No. 1, 1977

Recent Issues
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Generators of factors of Bernoulli shifts

Laif Swanson

Vol. 71 (1977), No. 1, 213–220
Abstract

One of the questions of ergodic theory is that of “relative position” of factors of Bernoulli shift. If 0 and 1 are factor algebras for a Bernoulli shift T, under what conditions is there an isomorphism ϕ commuting with T such that ϕ0 = 1?

In this paper, we give an example of a Bernoulli shift T of a space X and uncountably many partitions {Qα : α A} of X with the properties:

  1. (T,Qα}(T,Qβ) for α,β A.
  2. −∞TiQα is maximal for its entropy whenever α A.
  3. There is no isomorphism ϕ commuting with T such that ϕQα = Qβ unless α = β.

Mathematical Subject Classification
Primary: 28A65, 28A65
Milestones
Received: 17 May 1976
Published: 1 July 1977
Authors
Laif Swanson