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...

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

Finite-dimensional von Neumann algebra von Neumann architecture von Neumann bicommutant theorem von Neumann bounded set Von Neumann bottleneck von Neumann cardinal...

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

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...

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...

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

affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study...

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...

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...

the canonical example of a commutative von Neumann algebra. For this reason, the theory of von Neumann algebras is sometimes referred to as noncommutative...

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...

crossed product is a basic method of constructing a new von Neumann algebra from a von Neumann algebra acted on by a group. It is related to the semidirect...

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...

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...

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...

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...

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...

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...

interval [ 0 , 1 ] {\displaystyle [0,1]} . Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous...

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

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)....

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...

closed under taking adjoints. These include C*-algebras, von Neumann algebras, and AW*-algebras. C*-algebras can be easily characterized abstractly by a...

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...

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...

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...