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 note explains
the following topics: Metric and topological spaces, Banach spaces, Consequences
of Baire's Theorem, Dual spaces and weak topologies, Hilbert spaces, Operators
in Hilbert spaces, Banach algebras, Commutative Banach algebras, and Spectral
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: Hahn-Banach Theorems and
Introduction to Convex Conjugation, Baire Category Theorem and Its Application,
Weak Topology, Bounded (Linear) Operators and Spectral Theory, Compact and
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 explains the following topics:Operator Algebras, Linear
functionals on an operator algebra, Kaplansky's Density Theorem, Positive
continuous linear functionals, Disjoint representations of a C* -algebra, The
Tomita-Takesaki Modular operator, The canonical commutation relations, The
algebraic approach to quantum theory, Local quantum theory, The charged Bose
field and its sectors.
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.