References
Albeverio, S., Høegh-Krohn, R.: Frobenius theory for positive maps of von Neumann algebras. Comm. Math. Phys.64, 83–94 (1978)
Davies, E.B.: Quantum stochastic processes II. Comm. Math. Phys.19, 83–105 (1970). See also Davies, E.B.: Quantum theory of open systems (Chap. 6). New York-San Francisco-London: Academic Press 1976
Davies, E.B.: One-parameter semigroups. New York-San Francisco-London: Academic Press 1980
Evans, D.E.: Irreducible quantum dynamical semigroups. Comm. Math. Phys.54, 293–297 (1977)
Evans, D.E., Høegh-Krohn, R.: Spectral properties of positive maps onC *-algebras. J. London Math. Soc. (2)17, 345–355 (1978)
Evans, D.E., Lewis, J.T.: Dilations of irreversible evolutions in algebraic quantum theory. Comm. Dublin Inst. Adv. Studies. Ser. A24, 1977
Frigerio, A.: Quantum dynamical semigroups and approach to equilibrium. Lett. Math. Phys.2, 79–87 (1977)
Frigerio, A.: Stationary states of quantum dynamical semigroups. Comm. Math. Phys.63, 269–276 (1978)
Kossakowski, A., Frigerio, A., Gorini, V., Verri, M.: Quantum detailed balance and KMS condition. Comm. Math. Phys.57, 97–110 (1977)
Kümmerer, B., Nagel, R.J.: Mean ergodic semigroups onW *-algebras. Acta Sci. Math. (Szeged)41, 151–159 (1979). See also: Kümmerer, B.: Mean Ergodic Semigroups of contractions inW *-algebras. In: Group Theoretical Methods in Physics. Proceedings (Tübingen 1977), pp. 475–481. Lecture Notes in Physics79. Berlin-Heidelberg-New York: Springer 1978
Lindblad, G.: On the generators of quantum dynamical semigroups. Comm. Math. Phys.48, 119–130 (1976)
Nagel, R.J.: Mittelergodische Halbgruppen linearer Operatoren. Ann. Inst. Fourier (Grenoble)23, No. 4, 75–87 (1973). See also: Nagel, R.J.: Mean ergodic semigroups and invariant ideals in ordered Banach spaces. In: Foundations of Quantum Mechanics and Ordered Linear Spaces. Advanced Study Institute (Marburg 1973), pp. 309–315. Lecture Notes in Physics29. Berlin-Heidelberg-New York: Springer 1974
Spohn, H.: Approach to equilibrium for completely positive dynamical semigroups ofN-level systems. Rep. Mathematical Phys.10, 189–194 (1976)
Spohn, H.: An algebraic condition for the approach to equilibrium of an openN-level system. Lett. Math. Phys.2, 33–38 (1977)
Watanabe, S.: Ergodic theorems forW *-dynamical semigroups. Hokkaido Math. J.8, 176–190 (1979)
Watatani, Y., Enomoto, M.: A Perron-Frobenius type theorem for positive linear maps onC *-algebras. Math. Japan24, 53–63 (1979)
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Frigerio, A., Verri, M. Long-time asymptotic properties of dynamical semigroups onW *-algebras. Math Z 180, 275–286 (1982). https://doi.org/10.1007/BF01318911
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DOI: https://doi.org/10.1007/BF01318911