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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): 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
Posted: February 5, 2003
MathSciNet review: 1963750
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Abstract: Let $\triangle_T$ be an off-diagonal joining of a transformation . We construct a non-typical transformation having asymmetry between limit sets of $\triangle_{T^n}$ for positive and negative powers of . 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 in the weak closure (in the space of positive operators on ) of powers of Chacon's automorphism and its generalizations.

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