Mathematical Notes

, Volume 79, Issue 1, pp 3–17

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

  • G. G. Amosov
  • A. D. Baranov

DOI: 10.1007/s11006-006-0001-2

Cite this article as:
Amosov, G.G. & Baranov, A.D. Math Notes (2006) 79: 3. doi:10.1007/s11006-006-0001-2


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 WtIS2 (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 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • G. G. Amosov
    • 1
  • A. D. Baranov
    • 2
  1. 1.Moscow Institute of Physics and TechnologyMoscowRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia