Spectral Properties of Compact Operators

The spectral properties of a compact operatorT:X−→Yon a normed linear space resemblethose of square matrices. For a compact operator, the spectral properties can be treated fairlycompletely in the sense that Fredholm’s famous theory of integral equations may be extended tolinear functional equationsTx−λx=ywith a complex parameterλ. This paper has studiedand investigated the spectral properties of compact operators in Hilbert spaces. The spectralproperties of compact linear operators are relatively simple generalization of the eigenvalues offinite matrices. As a result, the paper has given a number of corresponding propositions andinteresting facts which are used to prove basic properties of compact operators. The Fredholmtheory has been introduced to investigate the solvability of linear integral equations involvingcompact operators.