Abstract
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.
Similar content being viewed by others
References
Schatten, R.: Norm ideals of completely continuous operators. Berlin, Göttingen, Heidelberg: Springer 1960
Uhlenbrock, D.: J. Math. Phys.12, 2503 (1971)
Angelescu, N., Nenciu, G., Bundaru, M.: Commun. Math. Phys.42, 29 (1975)
Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. II. Fourier analysis, self-adjointness. New York: Academic Press 1975
Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966
Bogolubov, N.N., jr.: Physica41, 601 (1969)
Maison, H.D.: Commun. Math. Phys.22, 166 (1971)
Zagrebnov, V.A., Brankov, J.G., Tonchev, N.S.: Dokl. Acad. Nauk USSR225, 71 (1975)
Hille, E., Phillips, R.S.: Functional analysis and semigroups. R.I., Providence: Amer. Math. Soc. Colloquium Publications 1957
Zagrebnov, V.A.: Ann. Phys. (N.Y.)102, 108 (1976)
Zagrebnov, V.A., in: Trans. Moscow Math. Soc. Vol.41, 121 Moscow: Moscow Univ. Press 1980 (in Russian)
Klauder, J.R.: Acta Phys. Austr. Suppl.XI, 341 (1973)
Simon, B.: J. Funct. Anal.14, 295 (1973)
Wehrl, A.: Reports Math. Phys.10, 159 (1976)
Simon, B.: Trace ideals and their applications. London Math. Soc. Lecture Notes Series 35. Cambridge: Cambridge University Press 1979
Author information
Authors and Affiliations
Additional information
Communicated by H. Araki
Rights and permissions
About this article
Cite this article
Zagrebnov, V.A. On the families of Gibbs semigroups. Commun.Math. Phys. 76, 269–276 (1980). https://doi.org/10.1007/BF02193557
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02193557