Abstract
We construct and discuss some explicit examples of Markov dilations for semigroups of completely positive operators on the W*-algebra of 2×2 matrices. In particular, we obtain a continuous Markov dilation for a semigroup of non-quasifree operators.
This paper reports on results which are part of a research project supported by the Deutsche Forschungsgemeinschaft
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Accardi, L.; Frigerio, A.; Lewis, J.T.: Quantum Stochastic Processes. Publ. RIMS, Kyoto Univ. 18 (1982), 97–133.
Emch, G.G.; Albeverio, S.; Eckmann, J.-P.: Quasi-Free Generalized K-Flows. Rep. Math. Phys. 13 (1978), 73–85.
Emch, G.G.; Varilly, J.C.: On the Standard Form of the Bloch Equation. Lett. Math. Phys. 3 (1979), 113–116.
Evans, D.E.: Completely Positive Quasi-Free Maps on the CAR Algebra. Comm. Math. Phys. 70 (1979), 53–68.
Hida, T.: Brownian Motion. Springer Verlag, Berlin-Heidelberg-New York 1980.
Kern, M.; Nagel, R.; Palm, G.: Dilations of Positive Operators: Construction and Ergodic Theory. Math. Z. 156 (1977), 256–277.
Kümmerer, B.: Markov Dilations of Completely Positive Operators on W*-Algebras. To appear in "Topics in Modern Operator Theory", Proc. Timisoara-Herculane 1982, Birkhäuser Verlag, Basel 1983.
Kümmerer, B.: A Dilation Theory for Completely Positive Operators on W*-Algebras. Thesis, Tübingen 1982.
Kümmerer, B.; Schröder, W.: A Markov Dilation of a Non-Quasifree Bloch Evolution. To appear in Comm. Math. Phys..
Kümmerer, B.; Schröder, W.: A Survey of Markov Dilations for the Spin-½-Relaxation and Physical Interpretation. Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 1981/82, 187–213.
Kümmerer, B.: A Non-Commutative Example of a Continuous Markov Dilation. Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 1982/83, 61–91.
Lewis, J.T.; Thomas, L.C.: How to Make a Heat Bath. In "Functional Integration", Proc. Cumberland Lodge, London, Clarendon Press, Oxford 1975, 97–123.
Sz.-Nagy, B.; Foias, C.: Harmonic Analysis of Operators on Hilbert Space. North Holland, Amsterdam 1970.
Varilly, J.C.: Dilation of a Non-Quasifree Dissipative Evolution. Lett. Math. Phys. 5 (1981), 113–116.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Kümmerer, B. (1984). Examples of markov dilations over the 2×2 matrices. In: Accardi, L., Frigerio, A., Gorini, V. (eds) Quantum Probability and Applications to the Quantum Theory of Irreversible Processes. Lecture Notes in Mathematics, vol 1055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071725
Download citation
DOI: https://doi.org/10.1007/BFb0071725
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12915-8
Online ISBN: 978-3-540-38798-5
eBook Packages: Springer Book Archive