Spectra of Compact Operators
César R. de Oliveira · 2025
Some general properties of the spectra of compact linear operators on Banach spaces are discussed. It is shown that, with the possible exception of zero, each eigenvalue of a compact operator has finite multiplicity, and the set of such eigenvalues can only accumulate at zero. The chapter then considers the important case of normal compact operators, particularly self-adjoint ones, on Hilbert spaces. It is shown that the eigenvectors of a normal operator can be chosen to form an orthonormal basis for the Hilbert space, which is used to present a version of the Spectral Theorem for normal operators.