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...

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...

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

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...

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...

In functional analysis, a state of an operator system is a positive linear functional of norm 1. States in functional analysis generalize the notion of...

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...

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...

(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...

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

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

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

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...

(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...

completely positive maps (channels) from A to Cn×n, where A is a C*-algebra and Cn×n denotes the n×n complex entries, and positive linear functionals (states)...

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...

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

In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological...

principle for ordered sets Order dual (functional analysis), set of all differences of any two positive linear functionals on an ordered vector space This disambiguation...

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...

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)...

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

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

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

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