Spectral Theory

Eigenvalues and Eigenvectors

Spectrum of an Operator

Resolvent Set

Resolvent Operator

Spectral Radius

Spectral Radius Formula

Properties of Spectrum

Spectral Mapping Theorem

Definition and Examples

Properties of Compact Operators

Space of Compact Operators

Spectral Theory of Compact Operators

Fredholm Alternative

Adjoint Operators

Self-Adjoint Operators

Properties of Self-Adjoint Operators

Spectral Theorem for Compact Self-Adjoint Operators

Spectral Theorem for Bounded Self-Adjoint Operators

Functional Calculus