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Unbounded gaps for cocycles and invariant measures for their Mackey actions

Author(s): Mariusz Lemanczyk; Sergey D. Sinel'shchikov
Journal: Proc. Amer. Math. Soc. 126 (1998), 815-818.
MSC (1991): Primary 28D05, 28D10
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Abstract: We show that for a class of type $\mathrm{III}_0$ -cocycles over a $\mathbb Z$ -action of type $\mathrm{II}_1$ its Mackey action must change the type.

References:

1.: I. P. Cornfeld, S. V. Sinai and Ya. G. Fomin, Ergodic Theory, Springer-Verlag, New York-Heidelberg-Berlin, 1982. MR 87f:28019
2.: V. Ya. Golodets and S. D. Sinelshchikov, Classification and structure of cocycles of amenable ergodic equivalence relations, J. Funct. Anal. 121 (1994), 455-485. MR 95h:28020
3.: T. Hamachi, Type $\mathrm{III}_0$ cocycles without unbounded gaps, Comment. Math. Univ. Carolinae 36 (1995), 713-720. MR 97b:28020
4.: M. Lema\'{n}czyk, Analytic nonregular cocycles over irrational rotations spaces, Comment. Math. Univ. Carolinae 36 (1995), 727-735. CMP 96:09
5.: K. Schmidt, Cocycles of Ergodic Transformation Groups, Lect. Notes in Math. Vol. 1, Macmillan Co. of India, 1977. MR 58:28262

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Additional Information:

Mariusz Lemanczyk
Affiliation: Department of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Torun, Poland
Email: mlem@mat.uni.torun.pl

Sergey D. Sinel'shchikov
Affiliation: Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, 310164 Kharkov, Ukraine
Email: sinelshchikov@ilt.kharkov.ua

DOI: 10.1090/S0002-9939-98-04121-5
PII: S 0002-9939(98)04121-5
Received by editor(s): January 9, 1996
Received by editor(s) in revised form: September 7, 1996
Additional Notes: The first author's research was partly supported by KBN grant 2 P301 031 07 (1994)
Communicated by: Mary Rees
Copyright of article: Copyright 1998, American Mathematical Society


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