A stochastic Stinespring Theorem

Mathematische Annalen

Volumn 319, Issue 4, 2001, Pages 647-673

  Goswami, Debashish ^a   Lindsay, J Martin ^b   Wills, Stephen J ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035607185     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004453     Document Type: Article

References (23)

1. V P Belavkin, Quantum stochastic calculus and quantum nonlinear filtering, J Multivariate Anal 42 (1992), 171-201.
2. V P Belavkin, Quantum stochastic positive evolutions: characterization, construction, dilation, Comm Math Phys 184 (1997), 533-566.
3. W S Bradshaw, Stochastic cocycles as a characterisation of quantum flows, Bull Sci Math (2) 116 (1992), 1-34.
4. P K Das and K B Sinha, Quantum flows with infinite degrees of freedom and their perturbations, in, "Quantum Probability and Related Topics VII," ed. L Accardi, World Scientific, Singapore (1992), 109-123.
5. J Dixmier, "Von Neumann algebras," North-Holland Publishing Co., Amsterdam, (1981).
6. M P Evans, Existence of quantum diffusions, Probab Theory Related Fields 81 (1989), 473-483.
7. M P Evans and R L Hudson, Perturbations of quantum diffusions, J London Math Soc 41 (1990), 373-384.
8. D E Evans and J T Lewis, Dilations of irreversible evolutions and algebraic quantum theory, Commun Dublin Inst Adv Studies Ser A 24 (1977).
9. F Fagnola, Characterization of isometric and unitary weakly differentiable cocycles in Fock space, in, "Quantum Probability and Related Topics VIII," ed. L Accardi, World Scientific, Singapore (1993).
10. D Goswami, J M Lindsay, K B Sinha and S J Wills, Dilation of Markovian cocycles on a von Neumann algebra, Pacific J. Math., to appear.
11. D Goswami and K B Sinha, Hilbert modules and stochastic dilation of a quantum dynamical semigroup on a von Neumann algebra, Comm Math Phys 205 (1999), 377-403.
12. U Haagerup, The Grothendieck inequality for bilinear forms on C*-algebras, Adv in Math 56 (1985), 93-116.
13. R L Hudson, Quantum diffusions and cohomology of algebras, in, "Proceedings of the First World Congress of the Bernoulli Society, Tashkent, USSR, Sept 1986," Vol. 1, eds. Yu V Prohorov and V V Sazonov, VNU Science Press, Utrecht (1987), 479-483.
14. R L Hudson and K R Parthasarathy, Quantum Itô's formula and stochastic evolutions, Comm Math Phys 93 (1984), 301-323.
15. J M Lindsay and K R Parthasarathy, On the generators of quantum stochastic flows, J Funct Anal 158 (1998), 521-549.
16. J M Lindsay and S J Wills, Existence, positivity and contractivity for quantum stochastic flows with infinite dimensional noise, Probab Theory Related Fields 116 (2000), 505-543.
17. J M Lindsay and S J Wills, Markovian cocycles on operator algebras, adapted to a Fock filtration, J Funct Anal, to appear.
18. J M Lindsay and S J Wills, Existence of Feller cocycles on a C*-algebra, Bull. London Math. Soc., to appear.
19. A Mohari, "Quantum Stochastic Calculus with Infinite Degrees of Freedom," PhD thesis, Indian Statistical Institute, Delhi (1992).
20. A Mohari and K B Sinha, Quantum stochastic flows with infinite degrees of freedom and countable state Markov processes, Sankhyā Ser A 52 (1990), 43-57.
21. K R Parthasarathy, "An Introduction to Quantum Stochastic Calculus," Birkhäuser, Basel (1992).
22. V I Paulsen, "Completely Bounded Maps and Dilations," Pitman Res Notes Math Ser 146, Longman Sci Tech, Harlow (1986).
23. W Stinespring, Positive functions on C*-algebras, Proc Amer Math Soc 6 (1955), 211-216.