von Neumann algebra


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von Neumann algebra

[fȯn ¦nȯi·män ′al·jə·brə]
(mathematics)
A subalgebra A of the algebra B (H) of bounded linear operators on a complex Hilbert space, such that the adjoint operator of any operator in A is also in A, and A is closed in the strong operator topology in B (H). Also known as ring of operators; W* algebra.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
([10]) proved that a Jordan centralizer on a CSL subalgebra of a von Neumann algebra is a centralizer.
A von Neumann algebra M is a concrete [C.sup.*]-algebra A (so A [subset[ B(H) for a Hilbert space H) which is closed with respect to the weak operator topology.
Since [[??].sub.p] is a von Neumann algebra and [mathematical expression not reproducible] is a Banach *-algebra, the tensor product [mathematical expression not reproducible] of (9.6) is a well-defined Banach *-algebra under product topology.
Recall that a finite von Neumann algebra A in B(H) is amenable if there is a state [phi] on B(H) which is A-central: [phi](ax) = [phi](xa) for a [member of] A and x [member of] B(H).
If A is a von Neumann algebra and [epsilon] is a full self dual Hilbert A-module, then B([epsilon]) is a von Neumann algebra and B([epsilon]) and A are Morita equivalent as von Neumann algebras.
A Von Neumann algebra approach to quantum metrics/quantum relations.
In [141 Haagerup introduced a numerical constant [lambda]([mu]) [element of] [1,[infinity]] associated to any von Neumann algebra [mu].
A von Neumann algebra M has the weak fixed point property if and only if M is finite dimensional.
In Subsection 4.1 we also provide a proof that the tracial nonstandard hull of an internal von Neumann algebra is itself a von Neumann algebra.
Connes's paper [Co] on the generalization of CKM matrix) between two subalgebras of the von Neumann algebra of the group G: the image of the representation of the Hecke algebra and the algebra of the almost normal subgroup.
If L is a CSL, whose projections are contained in a von Neumann algebra N acting on a Hilbert space H, then A = N [intersection] Alg L is called a CSL subalgebra of the von Neumann algebra N.
A von Neumann algebra M is [sigma]-finite if it admits at most countably many orthogonal projections.