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＜電子ブック＞
Theory of Operator Algebras III / by Masamichi Takesaki
(Encyclopaedia of Mathematical Sciences ; 127)

版	1st ed. 2003.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2003
本文言語	英語
大きさ	XXII, 548 p : online resource
冊子体	Theory of operator algebras / M. Takesaki ; 1 - 3 : softcover
著者標目	*Takesaki, Masamichi author SpringerLink (Online service)
件　名	LCSH:Operator theory LCSH:Mathematical physics FREE:Operator Theory FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-10453-8

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