Riesz Representation Theorem

(Theory)

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What is Riesz representation theorem?

Riesz representation theorem, sometimes called Riesz–Fréchet representation theorem, named after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space. If the underlying field is the real numbers, the two are isometrically isomorphic; if the underlying field is the complex numbers, the two are isometrically anti-isomorphic. The (anti-) isomorphism is a particular natural one as will be described next; a natural isomorphism.

Technology Types

duality theoryexplanationintegral representationmathematical theoremprocesspropositionrepresentationstatementtheoremtheorems in analysistheorems in functional analysistheorythinking

Synonyms

Fréchet-Riesz theoremFréchet–Riesz theoremRiesz isomorphismRiesz markovRiesz-Frechet representation theoremRiesz-Fréchet representation theoremRiesz–Frechet representation theoremRiesz–Fréchet representation theorem

Translations

Darstellungssatz von Fréchet-Riesz (de)Representatiestelling van Riesz (nl)Riesz representationssats (sv)Rieszova věta o reprezentaci (cs)Teorema da representação de Riesz (pt)Teorema de representació de Riesz (ca)Teorema de representación de Riesz (es)Teorema di rappresentazione di Riesz (it)Théorème de représentation de Riesz (Fréchet-Riesz) (fr)Twierdzenie Riesza (przestrzenie Hilberta) (pl)Теорема представлений Риса (ru)Теорема Ріса (uk)리스 표현 정리 (ko)リースの表現定理 (ja)

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