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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] |
Richard Kadison
Richard Vincent Kadison (July 25, 1925 – August 22, 2018) was an American mathematician known for his contributions to the study of operator algebras. Career Born in New York City in 1925, Kadison was a Gustave C. Kuemmerle Professor in the Department of Mathematics of the University of Pennsylvania.Richard Kadison wins 1999 AMS Steele Prize. Department of Mathematics, . Accessed January 12, 2010. Kadison was a member of the U.S. National Academy of Sciences (elected in 1996), and a foreign mem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Ringrose
John Robert Ringrose (born 21 December 1932) is an English mathematician working on operator algebras who introduced nest algebras. He was elected a Fellow of the Royal Society in 1977. In 1962, Ringrose won the Adams Prize The Adams Prize is a prize awarded each year by the Faculty of Mathematics at St John's College to a UK-based mathematician for distinguished research in mathematical sciences. The prize is named after the mathematician John Couch Adams and wa .... Works * (with Richard V. Kadison): '' Fundamentals of the Theory of Operator Algebras'', 4 vols., Academic Press 1983, 1986, 1991, 1992 (2nd edn. American Mathematical Society 1997) * ''Compact non self-adjoint operators'', van Nostrand 1971 See also * Pisier–Ringrose inequality References * * English mathematicians Fellows of the Royal Society 1932 births Living people {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mathematical Gazette
''The Mathematical Gazette'' is a triannual peer-reviewed academic journal published by Cambridge University Press on behalf of the Mathematical Association. It covers mathematics education with a focus on the 15–20 years age range. The journal was established in 1894 by Edward Mann Langley as the successor to the ''Reports of the Association for the Improvement of Geometrical Teaching''. William John Greenstreet was its editor-in-chief for more than thirty years (1897–1930). Since 2000, the editor is Gerry Leversha. Editors-in-chief The following persons are or have been editor-in-chief: Abstracting and indexing The journal is abstracted and indexed in EBSCO databases, Emerging Sources Citation Index, Scopus Scopus is a scientific abstract and citation database, launched by the academic publisher Elsevier as a competitor to older Web of Science in 2004. The ensuing competition between the two databases has been characterized as "intense" and is c ..., and zbMA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C*-algebra
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous linear operators on a complex Hilbert space with two additional properties: * ''A'' is a topologically closed set in the norm topology of operators. * ''A'' is closed under the operation of taking adjoints of operators. Another important class of non-Hilbert C*-algebras includes the algebra C_0(X) of complex-valued continuous functions on ''X'' that vanish at infinity, where ''X'' is a locally compact Hausdorff space. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Algebra
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. Two basic examples of von Neumann algebras are as follows: *The ring L^\infty(\mathbb R) of essentially bounded measurable functions on the real line is a commutative von Neumann algebra, whose elements act as multiplication operators by pointwise multiplication on the Hilbert space L^2(\mathbb R) of square-integrable functions. *The algebra \mathcal B(\mathcal H) of all bounded operators on a Hilbert space \mathcal H is a von Neuma ... [...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] |