Titlebook: Operator Functions and Localization of Spectra; Michael I. Gil’ Book 2003 Springer-Verlag Berlin Heidelberg 2003 Eigenvalue.Hilbert space.

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4 Localization of Eigenvalues of Finite Matrices,gorin result for matrices, which are ”close” to triangular ones. In addition, we derive upper and lower estimates for the spectral radius. Under some restrictions, these estimates improve the Frobenius inequalities. Moreover, we present new conditions for the stability of matrices, which supplement

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7 Functions of Non-compact Operators,eaking, a .-triangular operator is a sum of a normal operator and a compact quasinilpotent one, having a sufficiently rich set of invariant subspaces. In particular, we consider the following classes of .-triangular operators: operators whose Hermitian components are compact operators, and operators

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9 Spectrum Localization of Nonself-adjoint Operators,ators. Numerous integral, integro-differential operators and infinite matrices can be represented in such a form. We investigate the invertibility conditions and bounds for the spectra of the mentioned operators.

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11 Relatively ,-Triangular Operators,e following property: .:=... is a Volterra operator in .. If, in addition, . has a maximal resolutions of the identity, then it is called a relatively .-triangular operator. Below we derive estimates for the resolvents of various relatively .-triangular operators and investigate spectrum perturbatio

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19 Zeros of Entire Functions,em: if the Taylor coefficients of two entire functions are close, how close are their zeros? In addition, we establish bounds for sums of the absolute values of the zeros in the terms of the coefficients of its Taylor series. These bounds supplement the Hadamard theorem.