| Theory of Operator Algebras III 2003 Edition Contributor(s): Takesaki, Masamichi (Author) |
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ISBN: 3540429131 ISBN-13: 9783540429135 Publisher: Springer OUR PRICE: $189.99 Product Type: Hardcover - Other Formats Published: November 2002 Annotation: Together with "Theory of Operator Algebras I, II" (EMS 124 and 125), this book, written by one of the most prominent researchers in the field of operator algebras, presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. It is is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on operator algebras and non-commutative geometry (see http: //www.springer.de/math/ems/index.html). The book provides essential and comprehensive information for graduate students and researchers in mathematics and mathematical physics. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Medical - Mathematics | Mathematical Analysis |
| Dewey: 512.556 |
| LCCN: 2003542762 |
| Series: Encyclopaedia of Mathematical Sciences |
| Physical Information: 1.42" H x 6.48" W x 9.38" (2.08 lbs) 548 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |