Spectral Theory for Perturbations of Bounded Diagonal Linear Operators

Abstract

Our main goal in this chapter consists of computing the spectrum of the class of bounded linear operators, \( A = D + F \) where D is a diagonal operator and F is a finite rank operator. In order to achieve that, we will make extensive use of the theory of Fredholm operators and the notion of essential spectrum. A few illustrative examples will be discussed at the end of the end of this chapter. Here, we mainly follow Diagana et al. [18].