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In operator algebras, the enveloping von Neumann algebra of a C*-algebra is a von Neumann algebra that contains all the operator-algebraic information about the given C*-algebra. This may also be called the universal enveloping von Neumann algebra, since it is given by a universal property; and (as always with von Neumann algebras) the term W*-algebra may be used in place of von Neumann algebra.
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the reason is the Stone–vonNeumann theorem: there is a unique unitary representation with given action of the central Lie algebra element z, up to a unitary...
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corresponding to an elliptic differential operator D in the universal envelopingalgebra of G, are analytic. Not only do smooth or analytic vectors form dense...
about is given in the universal envelopingalgebra article. Quantum deformations of the universal envelopingalgebra lead to the notion of quantum groups...
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claim that Dixmier originated the name vonNeumannalgebra for the operator algebras introduced by John vonNeumann, but Dixmier said in an interview that...
(G)^{\prime \prime }P.} Thus the commutant of π is generated as a vonNeumannalgebra by operators P ρ ( f ) P = ∫ G f ( g ) ( P ρ ( g ) P ) d g {\displaystyle...
respect to the largest possibly C*-norm gives its enveloping C*-algebra, called the group C*-algebra C*(G) of G. (Any C*-norm on L1(G) is bounded by the...
the subspace H0 of K-invariant vectors in H. Moreover, the abelian vonNeumannalgebra it generates on H0 is maximal Abelian. By spectral theory, there...