Vol. 71, No. 1, 1977

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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