Abstract
We prove the existence of isometric and unitary dilations of a class of semi-groups of completely positive maps on an algebra of operators on a Hilbert space. The result has relevance to the problem of embedding an open quantum mechanical system in a closed one.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abragam, A.: The principles of nuclear magnetism. Oxford: Clarendon Press 1961
Atherton, N. M.: Electron spin resonance. New York: Wiley 1973
Cooper, J. L. B.: Ann. Math.48, 827–842 (1947)
Davies, E. B.: Commun. math. Phys.15, 277–304 (1969)
Davies, E. B.: Z. Wahrscheinlichkeitstheorie verw. Gebiete23, 261–273 (1972)
Evans, D. E.: Commun. math. Phys.48, 15–22 (1976)
Gorini, V., Kossokowski, A., Sudarshan, E. C. G.: University of Texas at Austin preprint CPT 244 (1975)
Haken, H.: Laser theory. Handb. Phys. Vol.25/2c. Berlin-Heidelberg-New York: Springer 1970
Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966
Kossokowski, A.: Rep. Math. Phys.3, 247–274 (1972)
Kraus, K.: Ann. Phys. (N. Y.)64, 311–335 (1971)
Lindblad, G.: Commun. math. Phys.48, 119–130 (1976)
Masani, P.: Bull. Amer. Math. Soc.68, 624–632 (1962)
Primas, H.: Helv. Phys. Acta34, 36–57 (1961)
Sakai, S.:C*-algebras andW*-algebras. Berlin-Heidelberg-New York: Springer 1971
Stroescu, E.: Pacific J. Math.47, 257–262 (1973)
Szökefalvi-Nagy, B.: Acta Scientiarum Math. Szeged15, 104–114 (1954)
Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1965
Author information
Authors and Affiliations
Additional information
Communicated by H. Araki
Rights and permissions
About this article
Cite this article
Evans, D.E., Lewis, J.T. Dilations of dynamical semi-groups. Commun.Math. Phys. 50, 219–227 (1976). https://doi.org/10.1007/BF01609402
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01609402