Mathematical Notes

, Volume 79, Issue 1, pp 3-17

First online:

Dilations of Contraction Cocycles and Cocycle Perturbations of the Translation Group of the Line

  • G. G. AmosovAffiliated withMoscow Institute of Physics and Technology
  • , A. D. BaranovAffiliated withSt. Petersburg State University

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The class of contraction cocycles which can be dilated to unitary Markovian cocycles of a translation group S on the straight line is introduced. The class of cocycle perturbations of S by unitary Markovian cocycles W with the property W t IS 2 (the Hilbert—Schmidt class) is investigated. The results are applied to perturbations of Kolmogorov flows on hyperfinite factors generated by the algebra of canonical anticommutation relations.

Key words

translation group on the line contraction cocycle dilation of a contraction cocycle cocycle perturbation unitary Markovian cocycle perturbations of Kolmogorov flows