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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1968, Volume 3, Issue 4, Pages 415–419 (Mi mz6696)

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.

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English version:
Mathematical Notes, 1968, 3:4, 264–266

Bibliographic databases:

UDC: 513.88

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

Citation in format AMSBIB
\Bibitem{Gek68} \by M.~M.~Gekhtman \paper Localization of the spectrum of certain non-self-adjoint operators \jour Mat. Zametki \yr 1968 \vol 3 \issue 4 \pages 415--419 \mathnet{http://mi.mathnet.ru/mz6696} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=227796} \zmath{https://zbmath.org/?q=an:0164.16902|0153.45201} \transl \jour Math. Notes \yr 1968 \vol 3 \issue 4 \pages 264--266 \crossref{https://doi.org/10.1007/BF01159942}