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Theory of Operator Algebras III. Vol.3

  • Fester Einband
  • 548 Seiten
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to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated ... Weiterlesen
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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.

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Topic relevant to future research in mathematics and mathematical physics


From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." Acta Scientiarum Mathematicarum

XIII Ergodic Transformation Groups and the Associated von Neumann Algebras.- XIV Approximately Finite Dimensional von Neumann Algebras.- XV Nuclear C*-Algebras.- XVI Injective von Neumann Algebras.- XVII Non-Commutative Ergodic Theory.- XVIII Structure of Approximately Finite Dimensional Factors.- XIX Subfactors of an Approximately Finite Dimensional Factor of Type II1.- Notation Index.


Titel: Theory of Operator Algebras III. Vol.3
EAN: 9783540429135
ISBN: 978-3-540-42913-5
Format: Fester Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 548
Gewicht: 946g
Größe: H38mm x B243mm x T164mm
Jahr: 2002
Auflage: 2003

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