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 book covers the following topics
related to Functional Analysis :Basics of Metric Spaces, Basics of Linear
Spaces, Orthogonality, Duality of Linear Spaces, Fourier Analysis, Operators,
Spectral Theory, Compactness, The spectral theorem for compact normal operators,
Banach and Normed Spaces, Measure Theory, Integration, Functional Spaces,
Fourier Transform, Advances of Metric Spaces.
Author(s): Vladimir V. Kisil, School of
Mathematics, University of Leeds
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 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 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.