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Matematicheskie Zametki, 1968, Volume 3, Issue 4, Pages 415–419
(Mi mzm6696)
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Localization of the spectrum of certain non-self-adjoint operators
M. M. Gekhtman M. V. Lomonosov Moscow State University
Abstract:
Let the self-adjoint operator $A$ and the bounded operator $B$ be specified in Hilbert space $\mathscr H$. We let denote the spectral family of the operator $A$. If $\|(E-E_N)B\|^2+E_{-N}B\|^2\to 0$, then in the complex plane $z=\sigma+\tau$ there will exist the curve $|\tau|=f(\sigma)$, $\lim f(\sigma)=0$ for $\sigma\to\pm\infty$ such that the entire spectrum of the operator $A+B$ lies within the region $|\tau|\le f(\sigma)$. In particular, the condition of the theorem will be satisfied when $B$ is a completely continuous operator.
Received: 01.07.1967
Citation:
M. M. Gekhtman, “Localization of the spectrum of certain non-self-adjoint operators”, Mat. Zametki, 3:4 (1968), 415–419; Math. Notes, 3:4 (1968), 264–266
Linking options:
https://www.mathnet.ru/eng/mzm6696 https://www.mathnet.ru/eng/mzm/v3/i4/p415
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