Elementary Functional Analysis

Abstract

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.