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.
References in periodicals archive ?
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.
We construct representations of the Hecke algebra of a group G, relative to an almost normal subgroup [GAMMA], into the von Neumann algebra of the group G, tensor matrices.
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].
1 we also provide a proof that the tracial nonstandard hull of an internal von Neumann algebra is itself a von Neumann algebra.
A von Neumann algebra M is [sigma]-finite if it admits at most countably many orthogonal projections.
Popa's new research direction, completely revolutionized the part of Von Neumann algebra theory, closely related to ergodic theory" (Quoted from the presentation signed Elaine Kehoe).
This is well-known that A(G) is the predual of the group von Neumann algebra of G as a Banach space.
We relate the Haagerup property of G to the embedding of its von Neumann algebra L(G) as a strongly mixing subalgebra of some finite von Neumann algebra M in the sense of [9]: this means that, for all x, y [member of] M such that [E.
K < G whose associated von Neumann algebras have mixing properties which imply that L(K) is the von Neumann algebra generated by the normalizer of L(H) in L(G).
In [23], Johnson, Kadison, and Ringrose introduced a notion of amenability for von Neumann algebras which modified Johnson's original definition for Banach algebras in the sense that it takes the dual space structure of a von Neumann algebra into account.