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Von Neumann algebra Wikipedia ~ A von Neumann algebra that acts on a separable Hilbert space is called separable Note that such algebras are rarely separable in the norm topology The von Neumann algebra generated by a set of bounded operators on a Hilbert space is the smallest von Neumann algebra containing all those operators
von Neumann Algebra from Wolfram MathWorld ~ A nontrivial corollary of the socalled bicommutant theorem says that a nondegeneratesubalgebra of is a von Neumann algebra if and only if it is strongly closed This is further equivalent to a number of other analytic properties of and of Blackadar 2013 and due to its bijective equivalence is sometimes used as a definition for von Neumann algebras
Von Neumann algebra Encyclopedia of Mathematics ~ The operations of forming the tensor product both finite and infinite are also defined for von Neumann algebras A von Neumann algebra is called a factor if its centre consists of multiples of the identity Let be a von Neumann algebra and the set of its positive operators
Notes on von Neumann algebras Vanderbilt University ~ 11 BANACH AND C ALGEBRAS 5 Proof If kxk
A GENTLE INTRODUCTION TO VON NEUMANN ALGEBRAS FOR MODEL ~ What makes von Neumann algebras such a robust notion is the equivalence of the algebraic conditions in 1 and 2 of Corollary 112 with the topologicalconditions3and4 ProofofTheorem110 FixT 0 2A00wemustshowthatanybasicstrongly open neighborhood of T 0 intersects A We first deal with the special case
Math 209 von Neumann Algebras ~ as von Neumann algebras are to essentially bounded measurable functions This will be made precise later on but for now take it as an indication that the intuition will shift from topological spaces to measure spaces However von Neumann algebras also o er a noncommutative context to study many other mathematical
Introduction to von Neumann algebras Lecture 1 ~ In short a Calgebra is a closed subalgebra of which is closed in the norm and a von Neumann algebra is a Calgebra that contains the identity and is also closed in the strong operator topology There is another way to define von Neumann algebras Given a set we define the commutant of denoted to be for all
Von Neumann Algebras University of California Berkeley ~ Von Neumann Algebras Vaughan Jones 1 October 1 2009 1SupportedinpartbyNSFGrantDMS93–22675theMarsdenfundUOA520 andtheSwissNationalScienceFoundation
Von Neumann Algebras Vanderbilt University ~ Von Neumann Algebras Vaughan Jones 1 November 13 2015 1SupportedinpartbyNSFGrantDMS93–22675theMarsdenfundUOA520 andtheSwissNationalScienceFoundation
Abelian von Neumann algebra Wikipedia ~ Von Neumann algebras A on H B on K are spatially isomorphic or unitarily isomorphic if and only if there is a unitary operator U H → K such that ∗ In particular spatially isomorphic von Neumann algebras are algebraically isomorphic
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