Journal of Soviet Mathematics

, Volume 49, Issue 6, pp 1267–1269 | Cite as

Ergodic actions of abelian groups and properties of their joint actions

  • V. Ya. Golodets
  • A. I. Danilenko
Article
  • 23 Downloads

Abstract

The concept of joint action is introduced. The joint action of two ergodynamic, measure preserving actions of an arbitrary locally compact Abelian group on Lebesgue spaces is investigated. It is proved that it is ergodic with a pure point spectrum. The spectrum of the joint action is computed. For the proof the individual Emerson—Greenleaf theorem for amenable groups has been used. The results generalize the known theorem of T. Hamachi and M. Osikawa for the actions of groups of real numbers.

Keywords

Real Number Abelian Group Joint Action Measure Preserve Lebesgue Space 

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Literature cited

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. Ya. Golodets
  • A. I. Danilenko

There are no affiliations available

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