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...specifically [[functional analysis]], the '''barrier cone''' is a [[cone (linear algebra)|cone]] associated to any non-empty subset of a [[Banach space]]. ...thus, the barrier cone of ''K'' is precisely the set of continuous linear functionals ''ℓ'' for which ''σ''_''K''(''ℓ'') is finite. ...

...r an infinite [[Field (mathematics)|field]] ''k'' is a [[polynomial]] in [[linear functional]]s with coefficients in ''k''; i.e., it can be written as where the <math>\lambda_{i_j}: V \to k</math> are linear functionals and the <math>w_{i_1, \dots, i_n}</math> are vectors in ''W''. For example, ...

...''' (also called a '''complete set''') in a [[vector space]] is a set of [[linear functional]]s <math>T</math> with the property that if a vector <math>x \in ...or space]] <math>X</math> is a total set or '''fundamental set''' if the [[linear span]] of <math>T</math> is [[Dense set|dense]] in <math>X.</math><ref name ...

=== Antilinear functionals and the anti-dual === ...}, the map defined by {{math|''x'' ↦ ''B''(''x'', ''y'')}} is [[linear map|linear]], and for all {{math|''x'' ∈ ''H''}}, the map defined by {{math|''y'' ↦ '' ...

{{Short description|Statement about linear functionals and measures}} ...hematics, the '''Riesz–Markov–Kakutani representation theorem''' relates [[linear functional]]s on spaces of continuous functions on a [[locally compact spac ...

...tion can be exploited to obtain several criteria for determining whether a linear functional on the algebra is [[ultraweak topology|ultraweakly]] continuous. ===Bounded functionals of Φ(''A'')=== ...

...esake of the Gerstewitz functions or Gerstewitz [[Functional (mathematics)|functionals]] in [[vector optimization]] and its generalizations.{{r|gerstewitz}} | title = Gerstewitz functionals on linear spaces and functionals with uniform sublevel sets ...

...pological vector space|vector topologies]] that have some given space of [[linear functional]]s as their [[continuous dual space]]. {{Duality and spaces of linear maps}} ...

...eorem''' refers to a [[necessary and sufficient conditions]] for a [[cone (linear algebra)|cone]] to be equal to its [[polar cone|bipolar]]. The bipolar the ...th> (that is, the weakest TVS topology on <math>X</math> making all linear functionals in <math>X^{\prime}</math> continuous). ...

...pace|reflexive]] if and only if every [[Continuous function|continuous]] [[linear functional]]'s [[Dual norm|norm]] on <math>X</math> attains its [[supremum] ...topology|weakly compact]] if and only if the [[dual norm]] each continuous linear functional on <math>X</math> attains a maximum on <math>C.</math> ...

...onal is then said to ''expose'' <math>x</math>. There can be many exposing functionals for <math>x</math>. The set of exposed points of <math>C</math> is usually ...

...nals and cumulant generating functionals to discuss the effect of noise in linear systems, J. Sound & Vibration 1964 vol.1, no.3, pp. 229-238</ref> Its defin ...

...o ''P''. Normal fans have applications to [[polyhedral combinatorics]], [[linear programming]], [[tropical geometry]] and other areas of mathematics. Each normal cone ''C''_''F'' is defined as the set of linear functionals ''w'' such that the set of points ''x'' in ''P'' that maximize ''w''(''x'') ...

...]]. It is an orthogonal expansion for nonlinear [[functional (mathematics)|functionals]] closely related to the [[Volterra series]] and having the same relation t ...er A, we can write the output of the system as sum of a series of Wiener G-functionals ...

...<math>X</math> is the space <math>X^\star</math> of all linear continuous functionals <math>f:X\to\mathbb{C}</math> endowed with the topology of uniform converge ...th>M</math>. The dual space <math>{\mathcal O}^\star(M)</math> of analytic functionals on <math>M</math> with the topology of uniform convergence on bounded sets ...

...ional achieves its minimum on <math>C</math>. Thus, if <math>f</math> is a linear functional on <math>V</math> and <math>\alpha =\inf\{ f(c)\ \colon c\in C\} ...edu/~baggett/funcchap3.pdf TOPOLOGICAL VECTOR SPACES AND CONTINUOUS LINEAR FUNCTIONALS], Chapter III of FUNCTIONAL ANALYSIS, Lawrence Baggett, University of Color ...

...f a real [[Banach space]] <math>X.</math> Then the set of all [[continuous linear functional]]s <math>f</math> that achieve their supremum on <math>B</math> ...

...\leq)</math> into a preordered vector space <math>(Y, \leq)</math> is a [[linear operator]] <math>f</math> on <math>X</math> into <math>Y</math> such that f In other words, a positive linear operator maps the positive cone of the [[Domain of a function|domain]] into ...

...dual''' of an [[ordered vector space]] <math>X</math> is the set of all [[linear functional]]s on <math>X</math> that map order intervals, which are sets of ...[[vector lattice]] and <math>f</math> and <math>g</math> are order bounded linear forms on <math>X.</math> ...

...}}, which is the vector space <math>X^{\prime}</math> of continuous linear functionals on {{mvar|X}} endowed with the [[topology of uniform convergence]] on [[Top ...rime}_b</math>, which consists of all [[continuous function|continuous]] [[linear functional]]s <math>f : X \to \mathbb{F}</math> and is equipped with the [[ ...