Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 28D05, 28D20

Retrieve articles in all journals with MSC (1991): 28D05, 28D20


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
Email: hoffman@math.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02446-0
PII: S 0002-9947(99)02446-0
Received by editor(s): March 31, 1997
Published electronically: July 1, 1999
Article copyright: © Copyright 1999 American Mathematical Society