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Ergodic actions of Abelian groups with a discrete spectrum, and approximate transitivity. (English. Russian original) Zbl 0729.28013

J. Sov. Math. 52, No. 6, 3530-3533 (1990); translation from Teor. Funkts., Funkts. Anal. Prilozh. 51, 117-122 (1989).
The authors have studied ergodic actions of Abelian groups with discrete spectrum. They proved that if a locally compact separable Abelian group G acts transitively on the Lebesgue space, then it has a “strange rank one”.

MSC:

28D15 General groups of measure-preserving transformations
22D40 Ergodic theory on groups
46L55 Noncommutative dynamical systems
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References:

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[2] A. del Junco, ?Transformations with discrete spectrum are stacking transformations?, Can. J. Math.,28, No. 4, 836?839 (1976). · Zbl 0312.47003 · doi:10.4153/CJM-1976-080-3
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