Abstract

This paper is concerned with describing the spectrum of the difference operator with a constant operator coefficient , which is a bounded linear operator in a Banach space . It is assumed that acts in the weighted space , , of two-sided sequences of vectors from . The main results are obtained in terms of the spectrum of the operator coefficient and properties of the weight function.Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given.Bibliography: 23 titles.

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