Elementary Functional Analysis (repost)

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required.

The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

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
The Spectral Theorem for Normal Operators