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Transactions of the American Mathematical Society

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A $K$ counterexample machine

Author: Christopher Hoffman
Journal: Trans. Amer. Math. Soc. 351 (1999), 4263-4280
MSC (1991): Primary 28D05; Secondary 28D20
Published electronically: July 1, 1999
MathSciNet review: 1650089
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Abstract: We present a general method for constructing families of measure preserving transformations which are $K$ and loosely Bernoulli with various ergodic theoretical properties. For example, we construct two $K$ transformations which are weakly isomorphic but not isomorphic, and a $K$ transformation with no roots. Ornstein's isomorphism theorem says families of Bernoulli shifts cannot have these properties. The construction uses a combination of properties from maps constructed by Ornstein and Shields, and Rudolph, and reduces the question of isomorphism of two transformations to the conjugacy of two related permutations.

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Additional Information

Christopher Hoffman
Affiliation: The Hebrew University, Institute of Mathematics, Jerusalem, Israel
Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742

Received by editor(s): March 31, 1997
Published electronically: July 1, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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