Geodesic
Sufficient conditions for dissipative dynamical semigroups to be conservative
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 2, pp. 192-211 
A. M. Chebotarev. Sufficient conditions for dissipative dynamical semigroups to be conservative. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 2, pp. 192-211. http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a2/
@article{TMF_1989_80_2_a2,
     author = {A. M. Chebotarev},
     title = {Sufficient conditions for dissipative dynamical semigroups to~be~conservative},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {192--211},
     year = {1989},
     volume = {80},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a2/}
}
TY  - JOUR
AU  - A. M. Chebotarev
TI  - Sufficient conditions for dissipative dynamical semigroups to be conservative
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1989
SP  - 192
EP  - 211
VL  - 80
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a2/
LA  - ru
ID  - TMF_1989_80_2_a2
ER  - 
%0 Journal Article
%A A. M. Chebotarev
%T Sufficient conditions for dissipative dynamical semigroups to be conservative
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1989
%P 192-211
%V 80
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a2/
%G ru
%F TMF_1989_80_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Dynamic semigroup of completely positive mappings of a von Neumann algebra leaving the unit operator invariant is called conservative. Sufficient conditions for a dynamic semigroup to be conservative are obtained which make it possible to find the general viewpoint on the conservativity properties of classical and quantum processes.

[1] Gorini V., Kossakowski A., Sudarshan E. C. G., J. Math. Phys., 17:3 (1976), 821–825 | DOI | MR

[2] Lindblad G., Commun. Math. Phys., 48:2 (1976), 119–130 | DOI | MR | Zbl

[3] Davies E. B., Rep. Math. Phys., 11:2 (1977), 169–188 | DOI | MR | Zbl

[4] Kvantovye sluchainye protsessy i otkrytye sistemy, Mir, M., 1988 | MR

[5] Khasminskii R. Z., Teoriya veroyatn. i ee primen., 5:1 (1960), 196–214 | MR | Zbl

[6] Makkin G., Stokhasticheskie integraly, Mir, M., 1972 | MR

[7] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977 | MR

[8] Ichihara K., Lecture Notes in Math., 1203, Springer-Verlag, 1986, 75–89 | DOI | MR

[9] Chebotarev A. M., Teoriya veroyatn. i ee primen., 33:1 (1988), 25–39 | MR

[10] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[11] Bratelli U., Robinson D., Operatornye algebry i kvantovaya mekhanika, Mir, M., 1982 | MR

[12] Stinespring W. F., Proc. Amer. Math. Soc., 6:2 (1955), 211–218 | DOI | MR

[13] Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[14] Edvards R., Funktsionalnyi analiz, Mir, M., 1969