Communications in Mathematical Physics

, Volume 76, Issue 3, pp 269–276 | Cite as

On the families of Gibbs semigroups

  • V. A. Zagrebnov


The families of Gibbs semigroups with generators from conveniently bounded monotonous families of self-adjoint operators are proved to be compact in the trace-norm topology.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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  1. 1.
    Schatten, R.: Norm ideals of completely continuous operators. Berlin, Göttingen, Heidelberg: Springer 1960Google Scholar
  2. 2.
    Uhlenbrock, D.: J. Math. Phys.12, 2503 (1971)Google Scholar
  3. 3.
    Angelescu, N., Nenciu, G., Bundaru, M.: Commun. Math. Phys.42, 29 (1975)Google Scholar
  4. 4.
    Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. II. Fourier analysis, self-adjointness. New York: Academic Press 1975Google Scholar
  5. 5.
    Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966Google Scholar
  6. 6.
    Bogolubov, N.N., jr.: Physica41, 601 (1969)Google Scholar
  7. 7.
    Maison, H.D.: Commun. Math. Phys.22, 166 (1971)Google Scholar
  8. 8.
    Zagrebnov, V.A., Brankov, J.G., Tonchev, N.S.: Dokl. Acad. Nauk USSR225, 71 (1975)Google Scholar
  9. 9.
    Hille, E., Phillips, R.S.: Functional analysis and semigroups. R.I., Providence: Amer. Math. Soc. Colloquium Publications 1957Google Scholar
  10. 10.
    Zagrebnov, V.A.: Ann. Phys. (N.Y.)102, 108 (1976)Google Scholar
  11. 11.
    Zagrebnov, V.A., in: Trans. Moscow Math. Soc. Vol.41, 121 Moscow: Moscow Univ. Press 1980 (in Russian)Google Scholar
  12. 12.
    Klauder, J.R.: Acta Phys. Austr. Suppl.XI, 341 (1973)Google Scholar
  13. 13.
    Simon, B.: J. Funct. Anal.14, 295 (1973)Google Scholar
  14. 14.
    Wehrl, A.: Reports Math. Phys.10, 159 (1976)Google Scholar
  15. 15.
    Simon, B.: Trace ideals and their applications. London Math. Soc. Lecture Notes Series 35. Cambridge: Cambridge University Press 1979Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • V. A. Zagrebnov
    • 1
  1. 1.Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaUSSR

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