Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Unbounded gaps for cocycles
and invariant measures for their Mackey actions


Authors: Mariusz Lemanczyk and Sergey D. Sinel'shchikov
Journal: Proc. Amer. Math. Soc. 126 (1998), 815-818
MSC (1991): Primary 28D05, 28D10
MathSciNet review: 1423313
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • 1. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinaĭ, Ergodic theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 245, Springer-Verlag, New York, 1982. Translated from the Russian by A. B. Sosinskiĭ. MR 832433
  • 2. V. Ya. Golodets and S. D. Sinel′shchikov, Classification and structure of cocycles of amenable ergodic equivalence relations, J. Funct. Anal. 121 (1994), no. 2, 455–485. MR 1272135, 10.1006/jfan.1994.1056
  • 3. Toshihiro Hamachi, Type 𝐼𝐼𝐼₀ cocycles without unbounded gaps, Comment. Math. Univ. Carolin. 36 (1995), no. 4, 713–720. MR 1378692
  • 4. M. Lema\'{n}czyk, Analytic nonregular cocycles over irrational rotations spaces, Comment. Math. Univ. Carolinae 36 (1995), 727-735. CMP 96:09
  • 5. Klaus Schmidt, Cocycles on ergodic transformation groups, Macmillan Company of India, Ltd., Delhi, 1977. Macmillan Lectures in Mathematics, Vol. 1. MR 0578731

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28D05, 28D10

Retrieve articles in all journals with MSC (1991): 28D05, 28D10


Additional Information

Mariusz Lemanczyk
Affiliation: Department of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, 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: http://dx.doi.org/10.1090/S0002-9939-98-04121-5
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
Article copyright: © Copyright 1998 American Mathematical Society