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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 Christian Potzsche
This note explains the following topics: basic structures, Topological structures and boundary value problems.
Author(s): Munich University of Technology
73 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 and its applications
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.
Author(s): Amol Sasane
92 Pages
Functional Analysis by Alexander C. R. Belton
This note covers the following topics related to functional analysis: Normed Spaces, Linear Operators, Dual Spaces, Normed Algebras, Invertibility, Characters and Maximal Ideals.
Author(s): Alexander C. R. Belton
127 Pages