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## Theory of Operator Algebras II

Sznitman, S. Varadhan Eds.

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FAQ Policy. About this book 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 's and 's.

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## Theory of Operator Algebras II

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- Theory of Operator Algebras II (Encyclopaedia of Mathematical Sciences).
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Theory of Operator Algebras II. Masamichi Takesaki.

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.

## NSF Award Search: Award# - Operator Algebras, Representations, and Wavelets

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. 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. 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.