Geodesic
Localization of the spectrum of certain non-self-adjoint operators
Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 415-419 
M. M. Gekhtman. Localization of the spectrum of certain non-self-adjoint operators. Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 415-419. http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a5/
@article{MZM_1968_3_4_a5,
     author = {M. M. Gekhtman},
     title = {Localization of the spectrum of certain non-self-adjoint operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {415--419},
     year = {1968},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.