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On asymmetry of the future and the past for limit self-joinings

Author: Oleg N. Ageev
Journal: Proc. Amer. Math. Soc. 131 (2003), 2053-2062
MSC (2000): Primary 37Axx, 28D05, 28D15, 20M14, 47B65; Secondary 47A05, 47A15, 47Dxx, 60Gxx
Published electronically: February 5, 2003
MathSciNet review: 1963750
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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.

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Additional Information

Oleg N. Ageev
Affiliation: Department of Mathematics, Moscow State Technical University, 2nd Baumanscaya St. 5, 105005 Moscow, Russia

Keywords: Joinings, Chacon's automorphism, weak operator convergence
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
Article copyright: © Copyright 2003 American Mathematical Society

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