This PDF book covers the
following topics related to Functional Analysis : The Axiom of Choice and Zornís
Lemma, Banach Spaces, Banach algebras and the Stone-Weierstrass Theorem, Hilbert
Spaces, Linear Operators, Duality, Spectral Theory.
Author(s): Daniel Daners, School of
Mathematics and Statistics, University of Sydney
This PDF covers the following topics related to
Functional Analysis : Banach and Hilbert spaces, Bounded linear operators, Main
principles of functional analysis, Compact operators, Elements of spectral
theory, Self-adjoint operators on Hilbert space.
Author(s): Roman Vershynin, Department of Mathematics,
University of Michigan
Functional analysis plays an important
role in the applied sciences as well as in mathematics itself. These notes are intended to familiarize the student with the basic
concepts, principles andmethods of functional analysis and its applications, and
they are intended for senior undergraduate or beginning graduate students.
Topics covered includes: Normed and Banach spaces, Continuous maps,
Differentiation, Geometry of inner product spaces , Compact operators and
Approximation of compact operators.
This notes provides a brief introduction to Real and Functional Analysis.
It covers basic Hilbert and Banach space theory as well as basic measure theory
including Lebesgue spaces and the Fourier transform.
This note covers the following topics: Vector spaces and their
topology, Linear Operators and Functionals, The Open Mapping Theorem, Uniform
Boundedness Principle, The Closed Range Theorem, Weak Topologies, Compact
Operators and their Spectra, General Spectral Theory.
This note covers the following topics: Baire category, Non-existence of
functions of several variables, The principle of uniform boundedness, Zorn's
lemma and Tychonov's theorem, The Hahn-Banach theorem, Banach algebras, Maximal
ideals, Analytic functions, The Gelfand representation.
This note covers the following topics: Metric and Normed Spaces, Continuous Functions, The Contraction Mapping
Theorem, Topological Spaces, Banach Spaces, Hilbert Spaces,
Fourier Series, Bounded Linear Operators on a Hilbert Space, The
Spectrum of Bounded Linear Operators, Linear Differential
Operators and Green's Functions, Distributions and the Fourier
Transform, Measure Theory and Function Spaces, Differential
Calculus and Variational Methods.
This manuscript provides a brief introduction to Real and
(linear and nonlinear) Functional Analysis. Topics covered
includes: Banach and Hilbert spaces, Compact operators, The main
theorems about Banach spaces, Bounded linear operators, Lebesgue
integration, The Lebesgue spaces Lp, The Fourier transform,
Interpolation, The Leray-Schauder mapping degree, The stationary
Navier-Stokes equation and Monotone operators.
These notes are based on lectures given at King's
College London as part of the Mathematics MSc programme. Topics
covered includes: Topological Spaces, Nets, Product Spaces,
Separation, Vector Spaces, Topological Vector Spaces, Locally
Convex Topological Vector Spaces, Banach Spaces, The Dual Space of
a Normed Space and Frechet Spaces.