Criteria for stability of the point spectrum under completely continuous perturbations

L. N. Nikol'skaya

Leningrad Polytechnic Institute

Abstract: We show that a number $\lambda$ is an eigenvalue of the operator $T+C$ for an arbitrary compact perturbation $C$ if and only if the operator $T-\lambda I$ is semi-Fredholm and $\mathrm{ind}\,(T-\lambda I)>0$.

UDC: 513.88

Received: 17.10.1974

 English version: Mathematical Notes, 1975, 18:4, 946–949

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