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Mathematische Annalen

, Volume 319, Issue 4, pp 647–673 | Cite as

A stochastic Stinespring Theorem

  • Debashish Goswami
  • J. Martin Lindsay
  • Stephen J. Wills
Original article

Abstract.

Completely positive Markovian cocycles on a von Neumann algebra, adapted to a Fock filtration, are realised as conjugations of \(^*\)-homomorphic Markovian cocycles. The conjugating processes are affiliated to the algebra, and are governed by quantum stochastic differential equations whose coefficients evolve according to the \(^*\)-homomorphic process. Some perturbation theory for quantum stochastic flows is developed in order to achieve the above Stinespring decomposition.

Mathematics Subject Classification (1991): 47Dxx, 46L53, 81S25, 60H20, 81Q15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Debashish Goswami
    • 1
  • J. Martin Lindsay
    • 2
  • Stephen J. Wills
    • 2
  1. 1.Indian Statistical Institute (Delhi Centre), 7 SJS Sansanwal Marg, New Delhi 110016, India (e-mail: debashis@isid.ac.in) IN
  2. 2.School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK (e-mail: jml@maths.nott.ac.uk, sjw@maths.nott.ac.uk) GB

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