von Neumann algebra


Also found in: Wikipedia.

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 ?
A Von Neumann algebra approach to quantum metrics/quantum relations.
Then Weaver goes on to define a quantum relation on a von Neumann algebra to be a weak* closed operator bimodule over its commutant.
A third objective plans to construct, and analyze, new classes of models of local Conformal Nets of von Neumann Algebras by means of Vertex Operator Algebras; among them the Shorter Moonshine Net .
US) introduce select topics of the theory of finite von Neumann algebras and their von Neumann subalgebras, emphasizing maximal abelian self-adjoint subalgebras (MASAs).
In 1984, he unexpectedly discovered a connection between von Neumann algebras (mathematical techniques that play a role in quantum mechanics) and knot theory.
After an introduction of fundamental facts (including material on von Neumann algebras and Aarveson's extension theorem), this covers basic theory, such as nuclear and exact C*-algebras, tensor products, constructions, exact groups, amenable traces and Kirchberg's factorization property, quasidiagonal C&-algebras, AF imbeddability, and local reflexivity.
Jones of the University of California at Berkeley unexpectedly discovered a connection between von Neumann algebras -- mathematical techniques that play a role in quantum mechanics -- and braid theory.
Themes include wavelets and quantum theory, operator theory and harmonic analysis, non-commutative geometry, C* algebras, Von Neumann algebras, frames in Hilbert space, the Kadison-Singer conjecture, extensions and dilations, and multivariable operator theory.