Elements of Spectral Theory of Operators. Compact Operators

Abstract

In this chapter we address the following subjects: the spectrum and eigenvalues of an operator; the resolvent and non-emptyness of the spectrum; finite-rank operators, the approximation property and compactness in Banach spaces; compactness criteria for sets in specific spaces; definition and properties of compact operators; operators of the form \(I - T\) with T a compact operator; the structure of the spectrum of a compact operator.