Scientific-Research Institute for Planning of Computing Centers and Economic-Information Systems, Academy of Sciences of the USSR
Abstract:
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.
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