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Fundamentals Of The Theory Of Operator Algebras
''Fundamentals of the Theory of Operator Algebras'' is a four-volume textbook on the classical theory of operator algebras written by Richard Kadison and John Ringrose. The first two volumes, published in 1983 and 1986, are entitled (I) ''Elementary Theory'' and (II) ''Advanced Theory''; the latter two volumes, published in 1991 and 1992, present complete solutions to the exercises in volumes I and II. Contents * Volume I: Elementary Theory : Chapter 1. Linear spaces : Chapter 2. Basics of Hilbert Space and Linear Operators : Chapter 3. Banach Algebras : Chapter 4. Elementary C*-Algebra Theory : Chapter 5. Elementary von Neumann Algebra Theory * Volume II: Advanced Theory : Chapter 6. Comparison Theory of Projection : Chapter 7. Normal States and Unitary Equivalence of von Neumann Algebras : Chapter 8. The Trace : Chapter 9. Algebra and Commutant : Chapter 10. Special Representation of C*-Algebras : Chapter 11. Tensor Products : Chapter 12. Approximation by Matrix Algebras : Chapter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Algebras
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of operator algebras are often phrased in algebraic terms, while the techniques used are often highly analytic.''Theory of Operator Algebras I'' By Masamichi Takesaki, Springer 2012, p vi Although the study of operator algebras is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Overview Operator algebras can be used to study arbitrary sets of operators with little algebraic relation ''simultaneously''. From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator. In general, operator algebras are non-commutative rings. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |