Dilation of a class of quantum dynamical semigroups with unbounded generators on UHF algebras

Debashish Goswami; Lingaraj Sahu; Kalyan B. Sinha

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 3, page 505-522
  • ISSN: 0246-0203

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Goswami, Debashish, Sahu, Lingaraj, and Sinha, Kalyan B.. "Dilation of a class of quantum dynamical semigroups with unbounded generators on UHF algebras." Annales de l'I.H.P. Probabilités et statistiques 41.3 (2005): 505-522. <http://eudml.org/doc/77856>.

@article{Goswami2005,
author = {Goswami, Debashish, Sahu, Lingaraj, Sinha, Kalyan B.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {3},
pages = {505-522},
publisher = {Elsevier},
title = {Dilation of a class of quantum dynamical semigroups with unbounded generators on UHF algebras},
url = {http://eudml.org/doc/77856},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Goswami, Debashish
AU - Sahu, Lingaraj
AU - Sinha, Kalyan B.
TI - Dilation of a class of quantum dynamical semigroups with unbounded generators on UHF algebras
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 3
SP - 505
EP - 522
LA - eng
UR - http://eudml.org/doc/77856
ER -

References

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  1. [1] P.S. Chakraborty, D. Goswami, K.B. Sinha, A covariant quantum stochastic dilation theory. Stochastics in finite and infinite dimensions, in: Trends Math., Birkhäuser Boston, Boston, MA, 2001, pp. 89-99. Zbl0982.46056MR1797082
  2. [2] D. Goswami, K.B. Sinha, Hilbert modules and stochastic dilation of a quantum dynamical semigroup on a von Neumann algebra, Comm. Math. Phys.205 (2) (1999) 377-403. Zbl0935.46055MR1712583
  3. [3] D. Goswami, K.B. Sinha, Stochastic dilation of symmetric completely positive semigroups, Preprint, available at, http://xxx.lanl.gov/math-ph/0201005. 
  4. [4] D. Goswami, A.K. Pal, K.B. Sinha, Stochastic dilation of a quantum dynamical semigroup on a separable unital C * -algebra, Infin. Dimens. Anal. Quantum Probab. Relat. Top.3 (1) (2000) 177-184. Zbl1243.81103
  5. [5] R.L. Hudson, K.R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys.93 (3) (1984) 301-323. Zbl0546.60058MR745686
  6. [6] T. Matsui, Markov semigroups on UHF algebras, Rev. Math. Phys.5 (3) (1993) 587-600. Zbl0794.46049MR1240735
  7. [7] P.A. Meyer, Quantum Probability for Probabilist, Lecture Notes in Math., vol. 1538, Springer-Verlag, Heidelberg, 1993. Zbl0773.60098MR1222649
  8. [8] A. Mohari, Quantum stochastic differential equations with unbounded coefficients and dilations of Feller's minimal solution, Sankhyā Ser. A53 (3) (1991) 255-287. Zbl0751.60062MR1189771
  9. [9] A. Mohari, K.B. Sinha, Stochastic dilation of minimal quantum dynamical semigroup, Proc. Indian Acad. Sci. Math. Sci.102 (3) (1992) 159-173. Zbl0766.60119MR1213635
  10. [10] K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs Math., vol. 85, Birkhäuser, Basel, 1992. Zbl0751.60046MR1164866

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