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RECONSTRUCTION THEOREM FOR STATIONARY MONOTONE QUANTUM MARKOV PROCESSES
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 Title & Authors
RECONSTRUCTION THEOREM FOR STATIONARY MONOTONE QUANTUM MARKOV PROCESSES
Heo, Jae-Seong; Belavkin, Viacheslav P.; Ji, Un Cig;
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 Abstract
Based on the Hilbert -module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.
 Keywords
Hilbert -module;covariant representation;quantum stochastic process;quantum dynamical semigroup;
 Language
English
 Cited by
1.
Stochastic Processes and Spectral Analysis for Hilbert $$C^*$$ C ∗ -Module-Valued Maps, Bulletin of the Malaysian Mathematical Sciences Society, 2015  crossref(new windwow)
 References
1.
L. Accardi, A. Frigerio, and J. T. Lewis, Quantum stochastic processes, Publ. Res. Inst. Math. Sci. 18 (1982), no. 1, 97-133. crossref(new window)

2.
V. P. Belavkin, A reconstruction theorem for a quantum random field, Uspekhi Mat. Nauk 39 (1984), no. 2, 137-138.

3.
V. P. Belavkin, Reconstruction theorem for a quantum stochastic process, Theor. Math. Phys. 62 (1985), 275-289. crossref(new window)

4.
B. V. Bhat and K. R. Parthasarathy, Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory, Ann. Inst. H. Poincare Probab. Statist. 31(1995), no. 4, 601-651.

5.
B. V. Bhat and M. Skeide, Tensor product systems of Hilbert modules and dilations of completely positive semigroups, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), no. 4, 519-575.

6.
P. S. Chakraborty, D. Goswami, and K. B. Sinha, A covariant quantum stochastic dilation theory, Stochastics in finite and infinite dimensions, 89-99, Trends Math., Birkhauser, Boston, 2001.

7.
E. Christensen and D. Evans, Cohomology of operator algebras and quantum dynamical semigroups, J. London Math. Soc. (2) 20 (1979), no. 2, 358-368. crossref(new window)

8.
E. B. Davies, Quantum stochastic processes, Comm. Math. Phys. 15 (1969), 277-304. crossref(new window)

9.
E. B. Davies, Markovian master equations, Comm. Math. Phys. 39 (1974), 91-110. crossref(new window)

10.
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), no. 2, 377-403. crossref(new window)

11.
J. Heo, Completely multi-positive linear maps and representations on Hilbert $C^{\ast}$- modules, J. Operator Theory 41 (1999), no. 1, 3-22.

12.
J. Heo, Hilbert $C^{\ast}$-module representation on Haagerup tensor products and group systems, Publ. Res. Inst. Math. Sci. 35 (1999), no. 5, 757-768. crossref(new window)

13.
J. Heo, V. P. Belavkin, and U. C. Ji, Monotone quantum stochastic processes and covariant dynamical hemigroups, J. Func. Anal. 261 (2011), 3345-3365. crossref(new window)

14.
E. Lance, Hilbert $C^{\ast}$-modules, Cambridge University Press, 1995.

15.
G. Lindblad, On the generators of quantum dynamical semigroups, Comm. Math. Phys. 48 (1976), no. 2, 119-130. crossref(new window)

16.
G. Lindblad, Non-Markovian quantum stochastic processes and their entropy, Comm. Math. Phys. 65 (1979), no. 3, 281-294. crossref(new window)

17.
K. Parthasarathy, A continuous time version of Stinespring's theorem on completely positive maps, Quantum probability and applications, V (Heidelberg, 1988), 296-300, Lecture Notes in Math., 1442, Springer, Berlin, 1990.

18.
W. Paschke, Inner product modules over $B^{\ast}$-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468.