Localization of the spectrum of certain non-self-adjoint operators |
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Authors: | M M Gekhtman |
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Institution: | (1) M. V. Lomonosov Moscow State University, USSR |
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Abstract: | Let the self-adjoint operator A and the bounded operator B be specified in Hilbert space We let denote the spectral family of the operator A. If (E – E
N
) B 2+E–NB 2 0 npnN , then in the complex plane z=+ there will exist the curve ¦ ¦ =f (), limf () = 0 for ± such that the entire spectrum of the operator A+B lies within the region ¦ ¦ f(). In particular, the condition of the theorem will be satisfied when B is a completely continuous operator.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 415–420, April, 1968.The author expresses his appreciation to R. S. Ismagilov for his discussion of the results. |
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