Von Neumann algebras and local quantum theory Notes
Von Neumann algebras and local quantum theory Notes
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.
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
This
note covers the following topics related to functional analysis: Normed Spaces, Linear Operators, Dual Spaces, Normed Algebras, Invertibility,
Characters and Maximal Ideals.
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.