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In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space is a linear functional on so that for all positive elements that is it holds that In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements. The significance of positive linear functionals lies in results such as Riesz–Markov–Kakutani representation theorem.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Relation100031921 yago:WikicatFunctionsAndMappings
rdfs:label	Funcional lineal positiva (es) Positive linear functional (en) Função linear positiva (pt)
rdfs:comment	En análisis funcional, una funcional lineal f en una C* álgebra es positiva si siempre que A sea un elemento positivo de . Véase también: * teorema de representación de Riesz * elemento positivo * Datos: Q7233279 (es) Na matemática, especialmente em análise funcional, uma função linear positiva num (V, ≤) é uma função linear f em V desde que para todo elemento positivo v de V, implica que Em outras palavras, uma função linear positiva garante retornar valores não negativos para qualquer elemento positivo. O teorema da representação de Riesz é uma das maiores amostras da importância das funções positivas lineares na . (pt) In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space is a linear functional on so that for all positive elements that is it holds that In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements. The significance of positive linear functionals lies in results such as Riesz–Markov–Kakutani representation theorem. (en)
dcterms:subject	Functional analysis
Wikipage page ID	454930 (xsd:integer)
Wikipage revision ID	1119696712 (xsd:integer)
Link from a Wikipage to another Wikipage	Bornological space Riesz space Riesz–Markov–Kakutani representation theorem Compact space Complete space Complex number Complex numbers Mathematics Eigenvalue Fréchet space Operator system Ordered topological vector space Ordered vector space Locally compact Functional analysis Cauchy–Schwarz inequality Trace of a matrix Hausdorff space Square matrix Linear functional Absorbing set Functional analysis Support (mathematics) Borel regular measure C*-algebra Positive-definite matrix Continuous function (topology) Inner product Metrizable Sesquilinear form Normal cone (functional analysis) Topological vector lattice GNS construction Inductive limit Kadison, Richard Positive cone Positive element (ordered group) Semi-complete Sequentially complete topological vector space
sameAs	Positive linear functional Positive linear functional Positive linear functional Positive linear functional Positive linear functional Positive linear functional
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Em dbt:ISBN dbt:Reflist dbt:Sfn dbt:Functional_analysis dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Ordered_topological_vector_spaces dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels
has abstract	En análisis funcional, una funcional lineal f en una C* álgebra es positiva si siempre que A sea un elemento positivo de . Véase también: * teorema de representación de Riesz * elemento positivo * Datos: Q7233279 (es) In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space is a linear functional on so that for all positive elements that is it holds that In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements. The significance of positive linear functionals lies in results such as Riesz–Markov–Kakutani representation theorem. When is a complex vector space, it is assumed that for all is real. As in the case when is a C-algebra with its partially ordered subspace of self-adjoint elements, sometimes a partial order is placed on only a subspace and the partial order does not extend to all of in which case the positive elements of are the positive elements of by abuse of notation. This implies that for a C-algebra, a positive linear functional sends any equal to for some to a real number, which is equal to its complex conjugate, and therefore all positive linear functionals preserve the self-adjointness of such This property is exploited in the GNS construction to relate positive linear functionals on a C*-algebra to inner products. (en) Na matemática, especialmente em análise funcional, uma função linear positiva num (V, ≤) é uma função linear f em V desde que para todo elemento positivo v de V, implica que Em outras palavras, uma função linear positiva garante retornar valores não negativos para qualquer elemento positivo. O teorema da representação de Riesz é uma das maiores amostras da importância das funções positivas lineares na . (pt)
prov:wasDerivedFrom	wikipedia-en:Positive_linear_functional?oldid=1119696712&ns=0
page length (characters) of wiki page	8455 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Positive_linear_functional
is Link from a Wikipage to another Wikipage of	List of functional analysis topics Riesz–Markov–Kakutani representation theorem Cyclic and separating vector Gelfand–Naimark–Segal construction Continuous functions on a compact Hausdorff space State (functional analysis) Cauchy–Schwarz inequality Local quantum field theory Glossary of functional analysis C*-algebra Positive linear operator Metric tensor Stinespring dilation theorem Positive functional
is Wikipage redirect of	Positive functional
is foaf:primaryTopic of	wikipedia-en:Positive_linear_functional

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