Table of Contents

Normed Linear and Banach Spaces; Linear Operators; Quotient Spaces; Finite Dimensional Normed Spaces; Inner Product and Hilbert Spaces; The Hahn-Banach Theorem; Applications of the Hahn-Banach Theorem to Normed Spaces; The Uniform Boundedness Principle; Weak Convergence; The Open Mapping and Closed Graph Theorems; Projections; Schauder Basis; Transpose and Adjoints of Continuous Linear Operators; Compact Operators; The Fredholm Alternative; The Spectrum of an Operator; Subdivisions of the Spectrum; The Spectrum of a Compact Operator; Symmetric Linear Operators; The Spectral Theorem for Compact Symmetric Operators; Symmetric Operators with Compact Inverse; Bounded Self Adjoint Operators; Orthogonal Projections; Sesquilinear Functionals; The Spectral Theorem for Bounded Self Adjoint Operators; An Operational Calculus.