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Von Neumann algebras and local quantum theory Notes
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.
Author(s): Ivan F Wilde
88 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 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
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