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FUNCTIONAL ANALYSIS Douglas N. Arnold References
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.
Author(s): Douglas N. Arnold
36 Pages 
Introduction to Functional Analysis by Daniel Daners
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
123 Pages
Functional Analysis by Roman Vershynin
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
131 Pages
Functional Analysis by ETH Zurich
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
427 Pages
Functional Analysis by Christian Remling
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.
Author(s): Christian Remling
123 Pages