Geodesic
Structure of the point spectrum of a~linear operator
Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 149-158.

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In order that a set of complex numbers be the point spectrum of some linear operator in a separable Hilbert space it is necessary and sufficient that it be a set of type $F_\sigma$. 
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     title = {Structure of the point spectrum of a~linear operator},
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L. N. Nikol'skaya. Structure of the point spectrum of a~linear operator. Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 149-158. http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a15/