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...

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...

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...

John von Neumann, notable Hungarian-American mathematician, physicist, and computer scientist. Von Neumann algebra Von Neumann architecture Von Neumann conjecture...

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...

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...

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

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...

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

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...

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...

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)....

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...

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

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...

theorem Gelfand–Naimark–Segal construction Von Neumann algebra Abelian von Neumann algebra von Neumann double commutant theorem Commutant, bicommutant...

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 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...

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...

In mathematics and in theoretical physics, the Stone–von Neumann theorem refers to any one of a number of different formulations of the uniqueness of...

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...

canonical trace. In fact, corresponding to every tracial state on a von Neumann algebra there is a notion of Fuglede−Kadison determinant. For matrices over...

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...

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...

representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric...

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...

representation if and only if the center of the von Neumann algebra generated by π(A) is one-dimensional. A C*-algebra A is of type I if and only if any separable...

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 is...