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- Q944297 subject Q10129880.
- Q944297 subject Q8266681.
- Q944297 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.".
- Q944297 wikiPageWikiLink Q10129880.
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- Q944297 wikiPageWikiLink Q1068085.
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- Q944297 wikiPageWikiLink Q653658.
- Q944297 wikiPageWikiLink Q726210.
- Q944297 wikiPageWikiLink Q8266681.
- Q944297 wikiPageWikiLink Q967972.
- Q944297 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.".
- Q944297 label "Open mapping theorem (functional analysis)".