Geodesic
Operators, absolutely indefinitely bounded below, in spaces with indefinite metric
Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 301-305 
V. A. Senderov. Operators, absolutely indefinitely bounded below, in spaces with indefinite metric. Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 301-305. http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a7/
@article{MZM_1971_10_3_a7,
     author = {V. A. Senderov},
     title = {Operators, absolutely indefinitely bounded below, in spaces with indefinite metric},
     journal = {Matemati\v{c}eskie zametki},
     pages = {301--305},
     year = {1971},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $r$ be the spectral radius of an operator $\mathfrak{U}$, absolutely indefinitely bounded below. It is proved that $r\geqslant c^{1/\alpha}$, where $c$ is the exact lower bound of $\mathfrak{U}$ and $\alpha$ is a number occurring in the definition of the $I$-metric. A bound is obtained for the dimensionality of the direct sum of root lineals of $\mathfrak{U}$ ($c\geqslant1$), corresponding to eigenvalues whose absolute values are smaller than unity.