| 书目名称 | Theory of Operator Algebras II |
| 编辑 | Masamichi Takesaki |
| 视频video | |
| 概述 | Very comprehensive.Outstanding author.Topic very relevant to future research in mathematics and mathematical physics.Includes supplementary material: |
| 丛书名称 | Encyclopaedia of Mathematical Sciences |
| 图书封面 |  |
| 描述 | 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, IT 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 funct |
| 出版日期 | Book 2003 |
| 关键词 | C*-algebra; Operator algebra; algebra; ergodic transformation groups; mathematical physics; von Neumann a |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-662-10451-4 |
| isbn_softcover | 978-3-642-07689-3 |
| isbn_ebook | 978-3-662-10451-4Series ISSN 0938-0396 |
| issn_series | 0938-0396 |
| copyright | Springer-Verlag Berlin Heidelberg 2003 |
发表于 2025-3-21 17:06:48
