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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 
This paper elaborates a short course on derivations and projections on Jordan triples. It introduces nonassociative algebra, continuous cohomology, and quantum functional analysis.
Author(s): Bernard Russo
72 Pages
Functional analysis lecture notes
This note covers normed linear spaces, Banach spaces, Linear transformations, Integration, Hilbert spaces and fourier analysis.
Author(s): T B Ward, University of East Anglia
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 Zorns Lemma, Banach Spaces, Banach algebras and the StoneWeierstrass 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 Christian Remling
This note explains the following topics, Metric and topological spaces, Banach spaces, Consequences of Baires 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
This note covers the following topics, Metric and Normed Spaces, Continuous Functions, The Contraction Mapping Theorem, Topological Spaces, Banach Spaces, Hilbert Spaces, Fourier Series, Bounded Linear Operators on a Hilbert Space, The Spectrum of Bounded Linear Operators, Linear Differential Operators and Greens Functions, Distributions and the Fourier Transform, Measure Theory and Function Spaces, Differential Calculus and Variational Methods.
Author(s): John Hunter and Bruno Nachtergaele
NA Pages