This is a preview of subscription content, log in via an institution to check access.
Literature cited
B. Sz. Nagy and S. Foias, Harmonic Analysis of Operators in Hilbert Spaces, North-Holland, Amsterdam (1971).
I. S. Gokhberg and M. G. Krein, “On a description of the contraction operators that are similar to unitary operators,” Funkts. Anal. Prilozhen.,1, No. 1, 38–60 (1967).
M. G. Krein, “Analytic problems and results of the theory of linear operators in a Hilbert space,” in: Proceedings of the International Congress of Mathematicians [Russian translation], Mir, Moscow (1968), pp. 189–216.
L. A. Sakhnovich, “Dissipative operators with absolutely continuous spectrum,” Tr. Mosk. Mat. Obshch.,19, 211–270 (1968).
L. A. Sakhnovich, “Operators that are similar to unitary operators with absolutely continuous spectrum,” Funkts. Anal. Prilozhen.,2, No. 1, 51–63 (1968).
L. A. Sakhnovich, “Nonunitary operators with absolutely continuous spectrum,” Izv. Akad. Nauk SSSR, Ser. Mat.,33, No. 1, 52–64 (1969).
E. Hille and R. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc., Providence (1957).
B. Sz. Nagy, “On uniformly bounded linear transformations in Hilbert space,” Acta Sci. Math. Szeged,11, 152–157 (1947).
A. G. Postnikov, Tauberian Theory and Its Applications [in Russian], Vol. 144, Proceedings of V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Nauka, Moscow (1979).
V. I. Gorbachuk and M. L. Gorbachuk, “Bounary values of the solutions of certain classes of differential equations,” Mat. Sb.,102, No. 1, 124–150 (1977).
Yu. M. Berezanskii, “Some applications of spaces with negative norm,” Stud. Math., Ser. Specjalna,1, 25–26 (1963).
V. I. Gorbachuk and L. B. Fedorova, “On the operational calculus for certain classes of non-self-adjoint operators,” Ukr. Mat. Zh.,31, No. 1, 123–131 (1979).
T. Kato, “Wave operators and similarity for some non-self-adjoint operators,” Math. Ann.,162, 258–279 (1966).
S. N. Naboko, “On the separability of the spectral components of a non-self-adjoint operator,” Dokl. Akad. Nauk SSSR,239, No. 5, 1052–1055 (1978).
S. N. Naboko, “A functional model of perturbation theory and its applications to scattering theory,” Tr. Mat. Inst. im. V. A. Steklova Akad. Nauk SSSR,147, 86–114 (1980).
K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall, Englewood Cliffs (1972).
S. N. Naboko, “On the conditions for similarity to unitary and self-adjoint operators,” Funkts. Anal. Prilozhen.,18, No. 1, 16–27 (1984).
J. A. van Casteren, “Operators similar to unitary and self-adjoint ones,” Pac. J. Math.,104, No. 1, 241–255 (1983).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 37, No. 1, pp. 49–56, January–February, 1985.
Rights and permissions
About this article
Cite this article
Malamud, M.M. A criterion for the similarity of a closed operator to a self-adjoint operator. Ukr Math J 37, 41–48 (1985). https://doi.org/10.1007/BF01056850
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01056850