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to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. A factor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.
Operator algebras --- Algèbres d'opérateurs --- 517.986 --- banachalgebra --- dicht --- tensoren --- integralen --- duaal --- Von Neumann --- poolse ruimte --- c*-algebra --- topologie --- spoor --- borel --- commutant --- Algebras, Operator --- Operator theory --- Topological algebras --- Topological algebras. Theory of infinite-dimensional representations --- Operator algebras. --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Analytical spaces --- Algèbres d'opérateurs --- Operator theory. --- Mathematical physics. --- Operator Theory. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Functional analysis --- Mathematics --- Algèbres topologiques --- Algèbres topologiques. --- Algèbres topologiques.
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Analytical spaces --- C*-algebras --- Automorphisms --- 517.986 --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Group theory --- Symmetry (Mathematics) --- Topological algebras. Theory of infinite-dimensional representations --- C*-algebras. --- Automorphisms. --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Algebres topologiques --- C etoile-algebres --- C star algebres
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Analytical spaces --- 517.986 --- C*-algebras --- Fiber bundles (Mathematics) --- Bundles, Fiber (Mathematics) --- Continuous groups --- Fiber spaces (Mathematics) --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Topological algebras. Theory of infinite-dimensional representations --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- C*-algebras. --- Faisceaux fibrés (mathématiques) --- C*-algèbres --- C*-algèbres.
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Analytical spaces --- 517.986 --- Von Neumann algebras --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Topological algebras. Theory of infinite-dimensional representations --- Von Neumann algebras. --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Algebres topologiques --- Algebres de von neumann
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Analytical spaces --- Ordered algebraic structures --- Banach spaces --- Banach modules (Algebra) --- Categories (Mathematics) --- 517.986 --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Functions of complex variables --- Generalized spaces --- Banach algebras --- Modules (Algebra) --- Topological algebras. Theory of infinite-dimensional representations --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Analyse fonctionnelle --- Functional analysis --- Functional analysis. --- Catégories (mathématiques)
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Operator algebras --- 531.19 --- 517.9 --- Statistical mechanics --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Operator algebras. --- Quantum statistics. --- Statistical mechanics. --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 531.19 Statistical mechanics --- Algèbres d'opérateurs --- Mécanique statistique --- Statistique quantique --- Quantum statistics --- Quantum statistical mechanics --- Matrix mechanics --- Algebras, Operator --- Topological algebras --- Algèbres d'opérateurs --- 517.986 --- Mechanics --- Mechanics, Analytic --- Statistical physics --- Thermodynamics --- Wave mechanics --- Operator theory --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Analytical spaces --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- Mécanique statistique --- Algebres topologiques --- Mecanique quantique --- Mecanique statistique quantique --- C star algebres
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Analytical spaces --- Function algebras --- Banach algebras --- Algèbres de fonctions --- Banach, Algèbres de --- 517.98 --- Algebras, Function --- Analytic functions --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Functional analysis and operator theory --- Banach algebras. --- Function algebras. --- 517.98 Functional analysis and operator theory --- Algèbres de fonctions --- Banach, Algèbres de --- Fonctions de plusieurs variables complexes
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Comets have fascinated and awed humankind since ancient times. Of the thousands of comets recorded throughout history, those deemed to have been the most spectacular have been described in the accounts of eyewitnesses and often recorded in official documents. This book introduces you to the greatest of the greats, starting with the comet in 372 B. C. called "Aristotle’s Comet" and ending with the spectacular appearance of McNaught’s Comet in 2007. There is an introductory chapter explaining what comets are and how they are classified, and correcting a few popular misconceptions. Later in the book you will read about the different returns of Halley’s Comet and the Kreutz sungrazing group, often called the kamikaze comets. There is even a chapter on comets that were visible in broad daylight. This book is unique. There are a few books on comets that make passing reference to some of the more famous or spectacular objects of the past, and a few catalogs with long lists of comets. But little detailed and descriptive information is contained in either of these sources. This is a fascinating account, not only for astronomers at every level but also for readers of popular science. In an engaging way it pulls together a vast amount of information and offers rich anecdotal material that will entertain as well as inform you.
Comets. --- Comets --- Astrophysics --- Mathematical Theory --- Mathematics --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Solar system. --- Nuclear spaces (Functional analysis) --- Schwartz spaces. --- Tensor products. --- Nuclear spaces (Functional analysis). --- Physics. --- Observations, Astronomical. --- Astronomy --- Astronomy. --- Astronomy, Observations and Techniques. --- Popular Science in Astronomy. --- Observations. --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 512 --- 512 Algebra --- Algebra --- Analytical spaces --- Milky Way --- Near-Earth objects --- Operator algebras --- Congresses. --- Schwartz, Espaces de. --- Produits tensoriels. --- Astronomy—Observations. --- Astronomical observations --- Observations, Astronomical --- Espaces nucléaires (analyse fonctionnelle) --- Algèbres topologiques --- Topological algebras --- Algèbres topologiques. --- Espaces nucléaires (analyse fonctionnelle) --- Algèbres topologiques.
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