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Conditions under which an operator obtained as a perturbation of multiplication by the independent variable is spectral

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Abstract

Conditions are studied under which the perturbed operator of multiplication by the independent variable is spectral in the sense of Dunford and Bade.

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Literature cited

  1. V. E. Lyantse, “Completely regular perturbation of the continuous spectrum,” Matem.,82 (124), 126–156 (1970);84 (126), 141–158 (1971).

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  2. N. Dunford, “Survey of the theory of spectral operators,” in: Matematika,4, No. 1, 53–100 (1960).

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  3. J. Schwartz, “Some nonselfadjoint operators,” Comm. Pure Appl. Math.,13, 609–639 (1960).

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  4. V. E. Lyantse, “On a certain generalization of the concept of a spectral measure,” Matem.,61 (103), 80–120 (1963).

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Authors and Affiliations

  1. L'vov State University, USSR

    V. É. Lyantse & I. P. Syroid

Authors
  1. V. É. Lyantse
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  2. I. P. Syroid
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Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 289–296, February, 1973.

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Lyantse, V.É., Syroid, I.P. Conditions under which an operator obtained as a perturbation of multiplication by the independent variable is spectral. Mathematical Notes of the Academy of Sciences of the USSR 13, 175–179 (1973). https://doi.org/10.1007/BF01094238

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  • DOI: https://doi.org/10.1007/BF01094238

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