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
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
Theorem.