On asymmetry of the future and the past for limit self-joinings
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- by Oleg N. Ageev PDF
- Proc. Amer. Math. Soc. 131 (2003), 2053-2062 Request permission
Abstract:
Let $\triangle _T$ be an off-diagonal joining of a transformation $T$. We construct a non-typical transformation having asymmetry between limit sets of $\triangle _{T^n}$ for positive and negative powers of $T$. It follows from a correspondence between subpolymorphisms and positive operators, and from the structure of limit polynomial operators. We apply this technique to find all polynomial operators of degree $1$ in the weak closure (in the space of positive operators on $L_2$) of powers of Chacon’s automorphism and its generalizations.References
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Additional Information
- Oleg N. Ageev
- Affiliation: Department of Mathematics, Moscow State Technical University, 2nd Baumanscaya St. 5, 105005 Moscow, Russia
- Email: ageev@mx.bmstu.ru
- Received by editor(s): April 19, 2001
- Published electronically: February 5, 2003
- Additional Notes: The author was supported in part by the Max Planck Institute of Mathematics, Bonn, and RFBR Grants #100-15-96107, #99-01-01104
- Communicated by: Michael Handel
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2053-2062
- MSC (2000): Primary 37Axx, 28D05, 28D15, 20M14, 47B65; Secondary 47A05, 47A15, 47Dxx, 60Gxx
- DOI: https://doi.org/10.1090/S0002-9939-03-06796-0
- MathSciNet review: 1963750