Abstract
A survey of the recent work on the infinitesimal generators of one-parameter semigroups of positivity preserving maps on operator algebras, in the presence of compact symmetry groups or flows.
Similar content being viewed by others
References
Alicki, R.:Rep. Math. Phys. 10 (1976), 249.
Araki, H.:Publ. RIMS Kyoto Univ. 8, (1972–73), 439.
Araki, H., Haag, R., Kastler, D., and Takesaki, M.:Commun. Math. Phys. 53 (1977), 97.
Arendt, W., Chernoff, P. R., and Kato, T.:J. Operator Theory 8, (1982), 167.
Batty, C. J. K.:Proc. London Math. Soc. (3)42 (1981), 299.
Batty, C. J. K., Carey, A. L., Evans, D. E., and Robinson, D. W.: Publ.RIMS Kyoto Univ. (to appear).
Berg, C. and Forst, G.:Potential Theory on Locally Compact Abelian Groups, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
Bratteli, O.:On Dynamical Semigroups and Compact Group Actions. Springer Lecture Notes in Mathematics. (ed. L. Accardi), to appear.
Bratteli, O., Digernes, T., and Robinson, D. W.: Positive semigroups on ordered Banach spaces'.
Bratteli, O., Digernes, T., Robinson, D. W.: ‘Relative locality of derivations’.
Bratteli, O., Elliott, G. A., and Evans, D. E.: ‘Locality and differential operators onC *-algebras’.
Bratteli, O., Elliott, G. A., and Jørgensen, P. E. T.:J. Reine Angew. Math. 346 (1984), 166–193.
Bratteli, O. and Evans, D. E.:Ergodic Theory and Dynamical Systems 3 (1983), 187–217.
Bratteli, O., Goodman, F., and Jørgensen, P. E. T.: ‘Unbounded derivations tangential to compact groups of automorphisms III’. Preprint.
Bratteli, O. and Jørgensen, P. E. T.:Proc. Symp. in Pure Math. Part 2, AMS, Providence RI, 1980, pp. 353–365.
Bratteli, O. and Jørgensen, P. E. T.:J. Funct. Anal. 48 (1982), 107.
Bratteli, O. and Jørgensen, P. E. T.:Commun. Math. Phys. 87 (1982), 353.
Bratteli, O., Jørgensen, P. E. T., Kishimoto, A. and Robinson, D. W.: ‘AC *-algebraic Schoenberg Theorem’. Preprint 1983. To appear inAnn. Inst. Fourier (Grenoble).
Bratteli, O., and Robinson, D. W.:Operator Algebras and Quantum Statistical Mechanics. I, Springer-Verlag, New York, 1979.
Bratteli, O. and Robinson, D. W.:Operator Algebras and Quantum Statistical Mechanics. II. Springer-Verlag, New York 1981.
Bratteli, O. and Robinson, D. W.:Math. Scand. 49 (1981), 259.
Choi, M. D.:Can. J. Math. 24 (1972), 520.
Choi, M. D.:Illinois J. Math. 18 (1974), 18.
Choi, M. D.:Linear Algebra and Appl. 10 (1974), 285.
Choi, M. D.:J. Operator Theory 4 (1980), 271.
Christensen, E. and Evans, D. E.:J. London Math. Soc. (2)20, (1978), 358.
Davies, E. B.:Quantum Theory of Open Systems, Academic Press, London, 1976.
Davies, E. B.:Rep. Math. Phys. 11 (1977), 169.
Davies, E. B.:J. Funct. Anal. 34 (1979), 421.
Davies, E. B.: ‘A generation theorem for operators commuting with group actions’.
Demoen, B., Vanheuverzwijn, P., and Verbeure, A.:Lett. Math. Phys. 2 (1977), 161.
Demoen, B., Vanheuverzwijn, P., and Verbeure, A.:Rep. Math. Phys.
Evans, D. E.:Commun. Math. Phys. 48 (1976), 15.
Evans, D. E.:Commun. Math. Phys. 54 (1977), 293.
Evans, D. E.:Quart J. Math. Oxford (2),28 (1977), 369.
Evans, D. E.: ‘Mathematical problems in the quantum theory of irreversible processes’, (eds. L. Accardi, V. Gorini, G. Parravicini), inProceedings of Arco Felice Conference, 1978, pp. 136–162.
Evans, D. E.:Commun. Math. Phys. 70 (1979), 53.
Evans, D. E.:J. Funct. Anal. 37 (1980), 318.
Evans, D. E.:Lecture Notes in Physics 116 (1980).
Evans, D. E.: ‘Operator algebras and applications’, in R. V. Kadison (ed.)Proc. Symp. Pure Math, Vol. 38, Amer. Math. Soc., Providence, RI, 1982, part 2, pp. 377–379.
Evans, D. E. Hanche-Olsen, H.:J. Funct. Anal. 32 (1979), 207.
Evans, D. E. and Hoegh-Krohn, R.:J. London Math. Soc. 17 (1978), 345.
Evans, D. E. and Lewis, J. T.:Commun. Math. Phys. 50 (1976), 219.
Evans, D. E. and Lewis, J. T.:J. Funct., Anal. 26 (1977), 369.
Evans, D. E. and Lewis, J. T.: ‘Dilations of irreversible evolutions in algebraic quantum theory’.Comm. Dubl. Inst. Adv. Studies, Ser. A 24, 1977.
Goodman, F. and Jørgensen, P. E. T.:Commun. Math. Phys. 82 (1981), 399.
Goodman, F. and Wasserman, A. J.: ‘Unbounded derivations commuting with compact group actions II’.J. Funct. Anal. 55 (1984), 389–397.
Gorini, V., Frigerio, A., Verri, M., Kossakowski, A., and Sudarshan, E. C. G.,Rep. Math. Phys. 12, (1977), 359.
Gorini, V., Frigerio, A., Verri, M., and Kossakowski, A.:Commun. Math. Phys. 57 (1977), 97.
Gorini, V., Kossakowski, A., and Sudarshan, E. C. G.:J. Math. Phys. 17 (1976), 821.
Ikunishi, A.: ‘Derivations inC *-algebras commuting with compact actions’,Publ. RIMS 19 (1983), 99–106.
Jørgensen, P. E. T.:Z. Wahrscheinlickstheorie Verw Gebiete. 63 (1983), 17.
Kadison, R. V.:Ann. Math. (2)56 (1952), 494.
Kadison, R. V.:Ann. Math. 83 (1966), 280.
Kishimoto, A.:Commun. Math. Phys. 47 (1976), 25.
Kishimoto, A. and Robinson, D. W.:Publ. RIMS Kyoto Univ.
Kraus, K.:Ann. Phys. 64 (1971), 311.
Kumjian, A.:Semestericht Funktionalysis, Tübingen Wintersemester 1982/83. pp. 179–191.
Lieb, E. H. and Ruskai, M. B.:Adv. Math. 12 (1974), 269.
Lindblad, G.:Commun. Math. Phys. 48 (1976), 119.
Lindblad, G.:Lett. Math. Phys. 1 (1976), 219.
Longo, R. and Peligrad, C.: ‘Non-commutative topological dynamics and compact actions onC *-algebras’ Preprint, 1983.
Nagel, R. and Uhlig, H.:J. Operator Theory. 6 (1981), 113.
Naimark, M. A.:C. R. (Doklady) Acad. Sci. URSS (N. S.) 41 (1943) 359.
Naimark, M. A.:Bull. Acad. Sci. URSS Ser. Math. 1 (1943), 237.
Peligrad, C.:Topics in Modern Operator Theory, OT Series Vol. 2, Birkhauser-Verlag, Basle, 1981, pp. 259–268.
Peligrad, C.: OT Series Vol. 6, Birkhauser-Verlag, Basle, 1982, pp. 181–194.
Powers, R. T. and Price, G. L.:Commun. Math. Phys.,84 (1982), 439.
Price, G. L.:Publ. RIMS Kyoto Univ. 19 (1983), 345.
Price, G. L.: ‘On derivations annihilating a maximal abelian subalgebra’.
Robinson, D. W.:Commun. Math. Phys. 85 (1982), 129.
Sakai, S.:Ann. Math. 83 (1966), 273.
Simon, B.:Indiana Univ. Math. J. 26 (1977), 1067.
Stinespring, W. F.:Proc. Amer. Math. Soc. 6 (1955), 211.
Størmer, E.:Acta Math. 110 (1963), 233.
Størmer, E.:Lecture Notes in Physics 29, Springer-Verlag, Berlin, 1974, pp. 85–106.
Stragier, G., Quaegebeur, J., and Verbeure, A.: ‘Quantum detailed balance’. Preprint, Leuven, 1983.
Takasaki, T. and Tomiyama, J.: ‘On the geometry of positive maps in matrix algebras’. Preprint, Niigata.
Takasaki, J. and Tomiyama, J.: Work in progress.
Takesaki, M.:Theory of Operator Algebras I. Springer-Verlag, New York, Heidelberg, Berlin, 1979.
Tsui, S. K.:Trans. Amer. Math. Soc. 66 (1977), 305.
Van Castersen, J. A.: ‘Invariant subsets of strongly continuous semigroups’. Preprint, Antwerp, 1983.
Vanheuverzwijn, P.:Ann. Inst. Poincaré 29 (1978), 123; Errata.30 (1979), 83.
Watanabe, S.: ‘Asymptotic behaviour and eigenvalues of dynamical semigroups on operator algebras’.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Evans, D.E. Quantum dynamical semigroups, symmetry groups, and locality. Acta Appl Math 2, 333–352 (1984). https://doi.org/10.1007/BF02280858
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02280858