functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication...

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string...

In functional analysis, a reflexive operator algebra A is an operator algebra that has enough invariant subspaces to characterize it. Formally, A is reflexive...

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 and contains...

of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:...

collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory. Single...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted...

spaces. Operators on these spaces are known as sequence transformations. Bounded linear operators over a Banach space form a Banach algebra in respect...

In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are...

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...

where ⟨S, ·, +, ′, 0, 1⟩ is a Boolean algebra and postfix I designates a unary operator, the interior operator, satisfying the identities: xI ≤ x xII...

different Poisson algebra, one that would be much larger. For a vertex operator algebra (V, Y, ω, 1), the space V/C2(V) is a Poisson algebra with {a, b} =...

non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

Vertex operator algebra Von Neumann algebra: a *-algebra of operators on a Hilbert space equipped with the weak operator topology. Algebraic structures...

is a closed *-subalgebra of the algebra of bounded operators on some Hilbert space. Measure algebra: A Banach algebra consisting of all Radon measures...

associative algebra of all bounded operators on a Hilbert space, together with the operator norm and the adjoint operation, yields a C*-algebra. Banach–Mazur...

group rings in representation theory, operator algebras in functional analysis, rings of differential operators, and cohomology rings in topology. The...

(\cdot ,\cdot )} . In the theory of operator algebras, the CCR algebra over H {\displaystyle H} is the unital C*-algebra generated by elements { W ( f ) :...

In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle...

now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

Finitary closure operators with this property give rise to antimatroids. As another example of a closure operator used in algebra, if some algebra has universe...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...

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 commute. The...

of relational algebra is to define operators that transform one or more input relations to an output relation. Given that these operators accept relations...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

theory, e.g. for operator-convex functions and operator algebras, where the domain and/or range are replaced by a C*-algebra or W*-algebra. An inner product...