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

Ageev, Oleg

doi:10.1090/S0002-9939-03-06796-0

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.

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