von Neumann algebras

E14972

*-algebra C*-algebra mathematical structure operator algebra

Von Neumann algebras are operator algebras of bounded operators on a Hilbert space that are closed in the weak operator topology and under taking adjoints, forming a central object in functional analysis and quantum theory.

Jump to: Surface forms Statements Referenced by

Observed surface forms (3)

Surface form	Occurrences
von Neumann algebra	0
W*-algebra	1
type II von Neumann algebra	1

Statements (52)

Predicate	Object
instanceOf	-algebra ⓘ C-algebra ⓘ mathematical structure ⓘ operator algebra ⓘ
alsoKnownAs	von Neumann algebras ⓘ surface form: W*-algebra
characterizedAs	C-algebra that is double commutant of a set of operators ⓘ C-algebra that is strong-operator closed ⓘ C*-algebra that is weak-operator closed ⓘ
classificationBy	type decomposition ⓘ
closedIn	strong operator topology ⓘ weak operator topology ⓘ
closedUnder	addition ⓘ adjoint operation ⓘ operator multiplication ⓘ scalar multiplication ⓘ
consistsOf	bounded linear operators ⓘ
contains	identity operator ⓘ
definedOn	Hilbert space ⓘ
field	functional analysis ⓘ mathematical physics ⓘ operator algebras ⓘ quantum theory ⓘ
hasKeyConcept	center ⓘ commutant ⓘ double commutant ⓘ factor ⓘ modular theory ⓘ normal state ⓘ predual ⓘ projection ⓘ trace ⓘ
hasOperation	conditional expectation ⓘ direct integral decomposition ⓘ
hasProperty	always has a unique predual up to isometry ⓘ closed in ultrastrong topology ⓘ closed in ultraweak topology ⓘ dual space of its predual ⓘ
hasType	type I von Neumann algebra ⓘ von Neumann algebras self-linksurface differs ⓘ surface form: type II von Neumann algebra type III von Neumann algebra ⓘ
introducedBy	John von Neumann ⓘ
relatedTo	Banach space ⓘ C*-algebra ⓘ Hilbert spaces ⓘ surface form: Hilbert space
subtype	hyperfinite II_1 factor ⓘ type III_λ factor ⓘ type II_1 factor ⓘ type II_∞ factor ⓘ
usedIn	algebraic quantum field theory ⓘ noncommutative geometry ⓘ noncommutative probability ⓘ quantum statistical mechanics ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

von Neumann algebras → alsoKnownAs → von Neumann algebras ⓘ

subject surface form: von Neumann algebra

this entity surface form: W*-algebra

Alain Connes → fieldOfWork → von Neumann algebras ⓘ

von Neumann algebras → hasType → von Neumann algebras self-linksurface differs ⓘ

subject surface form: von Neumann algebra

this entity surface form: type II von Neumann algebra

John von Neumann → knownFor → von Neumann algebras ⓘ