Abstract
We prove a theorem on an upper bound for the number of characteristic values of an operator-valued function that is holomorphic and bounded in a domain. This estimate is similar to the well-known inequality for zeros of a number function that is holomorphic and bounded in a domain. We derive several corollaries of the theorem proved, in particular, a statement on an estimate of the number of characteristic values of polynomial bundles of operators that lie in a given disk.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 211–224, February, 1998.
This work was financially supported by the Foundation for Fundamental Research of the Ukrainian Ministry of Science.
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Radzievskii, G.V. On an upper bound for the number of characteristic values of an operator function. Ukr Math J 50, 241–254 (1998). https://doi.org/10.1007/BF02513449
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DOI: https://doi.org/10.1007/BF02513449