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.
This PDF book covers the
following topics related to Functional Analysis : The Axiom of Choice and Zorn’s
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 note covers the following topics: Principles of Functional Analysis,
The Weak and Weak Topologies, Fredholm Theory, Spectral Theory, Unbounded
Operators, Semigroups of Operators.
Author(s): Theo Buhler and Dietmar A. Salamon, ETH
Zurich
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.