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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Approximation of commuting transformations

Authors: M. A. Akcoglu and R. V. Chacon
Journal: Proc. Amer. Math. Soc. 32 (1972), 111-119
MSC: Primary 28.70
MathSciNet review: 0289745
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Abstract: Let $ \sigma $ and $ \tau $ be two (measure-preserving) transformations. The main purpose of the paper is to show that if $ \tau $ admits approximation by partitions and that if $ \sigma $ commutes with a power $ {\tau ^s}$ of $ \tau $, then $ \sigma $ can be approximated by a finite number of powers of $ \tau $. As an application of the result we solve a problem posed earlier, showing that there exist strongly mixing transformations with only a finite number of prescribed roots.

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Keywords: Measure-preserving transformations, ergodic theory, commuting transformations
Article copyright: © Copyright 1972 American Mathematical Society