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- Open_mapping_theorem_(functional_analysis) abstract "In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is surjective then it is an open map. More precisely, (Rudin 1973, Theorem 2.11): Open Mapping Theorem. If X and Y are Banach spaces and A : X → Y is a surjective continuous linear operator, then A is an open map (i.e. if U is an open set in X, then A(U) is open in Y).The proof uses the Baire category theorem, and completeness of both X and Y is essential to the theorem. The statement of the theorem is no longer true if either space is just assumed to be a normed space, but is true if X and Y are taken to be Fréchet spaces.".
- Open_mapping_theorem_(functional_analysis) wikiPageID "17395276".
- Open_mapping_theorem_(functional_analysis) wikiPageRevisionID "601780901".
- Open_mapping_theorem_(functional_analysis) hasPhotoCollection Open_mapping_theorem_(functional_analysis).
- Open_mapping_theorem_(functional_analysis) id "8537".
- Open_mapping_theorem_(functional_analysis) title "Proof of open mapping theorem".
- Open_mapping_theorem_(functional_analysis) subject Category:Articles_containing_proofs.
- Open_mapping_theorem_(functional_analysis) subject Category:Functional_analysis.
- Open_mapping_theorem_(functional_analysis) subject Category:Theorems_in_functional_analysis.
- Open_mapping_theorem_(functional_analysis) type Abstraction100002137.
- Open_mapping_theorem_(functional_analysis) type Communication100033020.
- Open_mapping_theorem_(functional_analysis) type Message106598915.
- Open_mapping_theorem_(functional_analysis) type Proposition106750804.
- Open_mapping_theorem_(functional_analysis) type Statement106722453.
- Open_mapping_theorem_(functional_analysis) type Theorem106752293.
- Open_mapping_theorem_(functional_analysis) type TheoremsInFunctionalAnalysis.
- Open_mapping_theorem_(functional_analysis) comment "In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is surjective then it is an open map. More precisely, (Rudin 1973, Theorem 2.11): Open Mapping Theorem. If X and Y are Banach spaces and A : X → Y is a surjective continuous linear operator, then A is an open map (i.e.".
- Open_mapping_theorem_(functional_analysis) label "Open afbeeldingsstelling".
- Open_mapping_theorem_(functional_analysis) label "Open mapping theorem (functional analysis)".
- Open_mapping_theorem_(functional_analysis) label "Satz über die offene Abbildung".
- Open_mapping_theorem_(functional_analysis) label "Teorema de Banach-Schauder".
- Open_mapping_theorem_(functional_analysis) label "Teorema de la función abierta".
- Open_mapping_theorem_(functional_analysis) label "Teorema della funzione aperta (analisi funzionale)".
- Open_mapping_theorem_(functional_analysis) label "Théorème de Banach-Schauder".
- Open_mapping_theorem_(functional_analysis) label "Twierdzenie o odwzorowaniu otwartym".
- Open_mapping_theorem_(functional_analysis) label "Теорема об открытом отображении".
- Open_mapping_theorem_(functional_analysis) label "开映射定理".
- Open_mapping_theorem_(functional_analysis) label "開写像定理".
- Open_mapping_theorem_(functional_analysis) sameAs Satz_über_die_offene_Abbildung.
- Open_mapping_theorem_(functional_analysis) sameAs Teorema_de_la_función_abierta.
- Open_mapping_theorem_(functional_analysis) sameAs Théorème_de_Banach-Schauder.
- Open_mapping_theorem_(functional_analysis) sameAs Teorema_della_funzione_aperta_(analisi_funzionale).
- Open_mapping_theorem_(functional_analysis) sameAs 開写像定理.
- Open_mapping_theorem_(functional_analysis) sameAs 열린_사상정리_(함수해석학).
- Open_mapping_theorem_(functional_analysis) sameAs Open_afbeeldingsstelling.
- Open_mapping_theorem_(functional_analysis) sameAs Twierdzenie_o_odwzorowaniu_otwartym.
- Open_mapping_theorem_(functional_analysis) sameAs Teorema_de_Banach-Schauder.
- Open_mapping_theorem_(functional_analysis) sameAs m.04g1r1t.
- Open_mapping_theorem_(functional_analysis) sameAs Q944297.
- Open_mapping_theorem_(functional_analysis) sameAs Q944297.
- Open_mapping_theorem_(functional_analysis) sameAs Open_mapping_theorem_(functional_analysis).
- Open_mapping_theorem_(functional_analysis) wasDerivedFrom Open_mapping_theorem_(functional_analysis)?oldid=601780901.
- Open_mapping_theorem_(functional_analysis) isPrimaryTopicOf Open_mapping_theorem_(functional_analysis).