In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology...

functional analysis, a branch of mathematics, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements...

von Neumann algebra is a von Neumann algebra in which every isometry is a unitary. In other words, for an operator V in a finite von Neumann algebra if...

operators. These papers considered a special class of C*-algebras that are now known as von Neumann algebras. Around 1943, the work of Israel Gelfand and Mark...

Schatten–von Neumann norm Stone–von Neumann theorem Taylor–von Neumann–Sedov blast wave von Neumann algebra Abelian von Neumann algebra Enveloping von Neumann...

John von Neumann (/vɒn ˈnɔɪmən/ von NOY-mən; Hungarian: Neumann János Lajos [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian...

the *-algebras closed in these topologies. If M is closed in the norm topology then it is a C*-algebra, but not necessarily a von Neumann algebra. One...

of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in the series On Rings of Operators. One of von Neumann's...

infinite and one finite. Murray and von Neumann proved that up to isomorphism there is a unique von Neumann algebra that is a factor of type II1 and also...

mathematician Von Neumann family Von Neumann (surname), a German surname Von Neumann (crater), a lunar impact crater Von Neumann algebra Von Neumann architecture...

Von Neumann regular rings were introduced by von Neumann (1936) under the name of "regular rings", in the course of his study of von Neumann algebras...

September 2020) was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990. Jones...

In operator algebras, the enveloping von Neumann algebra of a C*-algebra is a von Neumann algebra that contains all the operator-algebraic information...

In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita–Takesaki theory is a method for constructing modular...

group C*-algebra defined above if and only if G is amenable. The group von Neumann algebra W*(G) of G is the enveloping von Neumann algebra of C*(G)....

of B(H) is a von Neumann algebra if, and only if, M = M ′ ′ {\displaystyle M=M^{\prime \prime }} , and that if not, the von Neumann algebra it generates...

algebra Enveloping algebra, of an associative algebra: see Associative algebra § Enveloping algebra Enveloping von Neumann algebra, of a C*-algebra This...

constant for a one-dimensional algebra is 1. Nest algebras are hyper-reflexive with distance constant 1. Many von Neumann algebras are hyper-reflexive, but...

a von Neumann algebra plus a representation and of a measure space) are mutually inverse. Von Neumann then proposed that non-commutative von Neumann algebras...

specific von Neumann algebra acting on a Hilbert space in the presence of a trace. The first such result was proved by Francis Joseph Murray and John von Neumann...

Von Neumann bicommutant theorem states that a *-subalgebra A of the algebra of bounded operators B(H) on a Hilbert space H is a von Neumann algebra (i...

defined). He proved that any such algebra is a Jordan algebra. Not every Jordan algebra is formally real, but Jordan, von Neumann & Wigner (1934) classified...

formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated in several...

subfactors of von Neumann algebras. Let R {\displaystyle R} be a commutative ring and fix δ ∈ R {\displaystyle \delta \in R} . The Temperley–Lieb algebra T L n...

Typically the random variables lie in a unital algebra A such as a C*-algebra or a von Neumann algebra. The algebra comes equipped with a noncommutative expectation...

For unital AF algebras, both existence and uniqueness follow from the fact the Murray-von Neumann semigroup of projections in an AF algebra is cancellative...

B*-algebra C*-algebra Dagger category von Neumann algebra Baer ring Operator algebra Conjugate (algebra) Cayley–Dickson construction Composition algebra...

C*-algebra S a topological space Ŝ; see spectrum of a C*-algebra. For the duality between localizable measure spaces and commutative von Neumann algebras...

give an algebraic analogue of von Neumann algebras, using axioms about annihilators of various sets. Any von Neumann algebra is a Baer *-ring, and much of...

of a cyclic and separating vector is important in the theory of von Neumann algebras, and, in particular, in Tomita–Takesaki theory. A related notion...