Geodesic
Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator
Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 403-412.

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We obtain asymptotic bounds for the perturbed eigenvalues and eigenvectors of a perturbed linear bounded operator $A(\varepsilon)$, in a Hilbert space under the assumption that $A(\varepsilon)$ is holomorphic at the point $\varepsilon=\varepsilon_0$ and the eigenvalue $\lambda_0=\lambda(\varepsilon_0)$ of the operator $A(\varepsilon_0)$ is isolated and of finite multiplicity. We study certain cases of high degeneracy in the limiting problem, i.e., the case when there are generalized associated vectors. 
@article{MZM_1972_12_4_a6,
     author = {Yu. Muratov},
     title = {Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--412},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a6/}
}
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Yu. Muratov. Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator. Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 403-412. http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a6/