specifically in functional analysis, a positive linear functional on an ordered vector space ( V , ≤ ) {\displaystyle (V,\leq )} is a linear functional f {\displaystyle...

In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

Hausdorff space and ψ {\displaystyle \psi } a positive linear functional on Cc(X). Then there exists a unique positive Borel measure μ {\displaystyle \mu } on...

In mathematics, more specifically in functional analysis, a positive linear operator from an preordered vector space ( X , ≤ ) {\displaystyle (X,\leq )}...

In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional...

element Ω of the Hilbert spaceH defines a positive linear functional ωΩ on a *-algebra A of bounded linear operators on H via the inner product ωΩ(a) = (aΩ...

mathematical field of functional analysis, a state of an operator system is a positive linear functional of norm 1. States in functional analysis generalize...

complex numbers. In functional analysis, the term linear functional is a synonym of linear form; that is, it is a scalar-valued linear map. Depending on...

C*-algebra or W*-algebra. An inner product can be used to define a positive linear functional. For example, given a Hilbert space L 2 ( m ) , m {\displaystyle...

C*-algebra Universal C*-algebra Spectrum of a C*-algebra Positive element Positive linear functional operator algebra nest algebra reflexive operator algebra...

Haar measure as a by-product. The functional μ A {\displaystyle \mu _{A}} extends to a positive linear functional on compactly supported continuous functions...

{\displaystyle *} -representations of A {\displaystyle A} and certain linear functionals on A {\displaystyle A} (called states). The correspondence is shown...

(controls), a term related to control theory State (functional analysis), a positive linear functional on an operator algebra State, in dynamical systems...

such a linear function from the other concept, the term affine function is often used. In linear algebra, mathematical analysis, and functional analysis...

(primitive causality). A state with respect to a C*-algebra is a positive linear functional over it with unit norm. If we have a state over A ( M ) {\displaystyle...

spectrum of a linear operator T {\displaystyle T} that operates on a Banach space X {\displaystyle X} is a fundamental concept of functional analysis. The...

Hausdorff spaces, and only consider the measures that correspond to positive linear functionals on the space of continuous functions with compact support (some...

be defined, by the Riesz representation theorem, by giving a positive linear functional Λ on the space C0(M) of compactly supported continuous functions...

In functional analysis and operator theory, a bounded linear operator is a special kind of linear transformation that is particularly important in infinite...

In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting...

be a convex cone. A linear functional ϕ : F → R {\displaystyle \phi :F\to \mathbb {R} } is called K {\displaystyle K} -positive, if it takes only non-negative...

f ) ≥ 0. {\displaystyle T(f)\geq 0.} One may show that every positive linear functional on C c 0 ( U ) {\displaystyle C_{c}^{0}(U)} is necessarily continuous...

Neumann algebra is a linear map from the set of positive elements (those of the form a*a) to [0,∞]. A positive linear functional is a weight with ω(1)...

isomorphism with the linear functional obtained above results in a linear functional on Hom(V, V). This linear functional is exactly the same as the trace...

nullity Rank–nullity theorem Nullity theorem Dual space Linear function Linear functional Category of vector spaces Topological vector space Normed...

In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative...

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

completely positive maps, rather than merely positive ones, are the true generalizations of positive functionals. A linear positive functional on a C*-algebra...

The generalized functional linear model (GFLM) is an extension of the generalized linear model (GLM) that allows one to regress univariate responses of...