Spectral properties of linear bounded operators containing uncertainty

In this thesis the srectrum and the resolvent sets of linear operators and operator penscils defined on a complex Banach space are considered. Such problems arise in the solutions of systems of linear equations, differential equations, integral equations which are important in applications. The thesis consists of the Introduction, nine paragraphs and the Reference list. In the second and third paragraphs invertible linear operators, bounded operators with closed ranges are defined, the Open Mapping Theorem and the Bounded Inverse Theorem ate formulated. The fourth paragraph contains the properties of self-adjoint, unitary and normal operators defined in a complex Hilbert space. In the fivth -seventh paragraphs the propersies of the spectrum and resolvent sets of bounded linear operators defined on finite and infinite dimensional Banach spaces. Here some connections between the resolvent set and the one-to-one, onto properties are established. The eighth paragraph contains the properties of the spectrum of a parametric operators defined on a finite dimensional normed space. In the nineth paragraph for an affine family of linear operators defined on a complex Hilbert space the conditions under which the spectrum is empty or is whole complex plane are considered. In the last paragraph one class of quadratic opertor pencil which is important in applications is considered. The conditions under which the spectrum is contained in the upper open, upper closed half planes, on the imajinary axis are given.