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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an off-diagonal joining of a transformation . We construct a non-typical transformation having asymmetry between limit sets of 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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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

DOI:
https://doi.org/10.1090/S0002-9939-03-06796-0

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