Abstract
Let A be the generator of a strongly continuous nonquasianatytic oneparameter group of operators U(t) (A, in general, is unbounded). In this case one proves a spectral mapping theorem in the following form:
. The proof is based on the theory of operators with separable spectrum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
D. E. Evans, “On the spectrum of a one-parameter strongly continuous representation,” Math. Scand.,39, 80–82 (1976).
W. Arendt and G. Greiner, Lecture Notes in Math., No. 1184, 90–93 (1986).
Yu. I. Lyubich and V. I. Matsaev, “On operators with separable spectrum,” Mat. Sb.,56, No. 4, 433–468 (1962).
E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc., Providence (1957).
M. G. Krein, M. A. Krasnosel'skii, and D. P. Mil'man, “On defect numbers of linear operators in a Banach space and on certain geometric questions,” Sbornik Trudov Inst. Mat. Akad Nauk USSR,11, 97–112 (1948).
J. Prüss, “On the spectrum of C0-semigroups,” Trans. Amer. Math. Soc.,284, No. 2, 847–857 (1984).
Yu. L. Daletskii (Ju. L. Daleckii) and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence (1974).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 146–150, 1989.
Rights and permissions
About this article
Cite this article
Fong, V.Q., Lyubich, Y.I. On the spectral mapping theorem for one-parameter groups of operators. J Math Sci 61, 2035–2037 (1992). https://doi.org/10.1007/BF01095666
Issue Date:
DOI: https://doi.org/10.1007/BF01095666