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In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space. The theorem also shows that there are sufficient continuous linear functionals defined on every normed vector space in order to study the dual space. Another…
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Hahn–Banach theorem | is a | central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space | 0.90 | text |
| Hahn–Banach theorem | is a | first sign of an important philosophy in functional analysis | 0.90 | text |
| the moment problem | instance of | This is needed to solve problems | 0.80 | text |
| whereby given all the potential moments of a function one must determine if a function having these moments exists | instance of | This is needed to solve problems | 0.80 | text |
| and | instance of | This is needed to solve problems | 0.80 | text |
| if so | instance of | This is needed to solve problems | 0.80 | text |
| find it in terms of those moments | instance of | This is needed to solve problems | 0.80 | text |
| Hahn–Banach theorem | has application | The Hahn | 0.60 | section |
| Hahn–Banach theorem | has application | Banach | 0.60 | section |
| Hahn–Banach theorem | has application | For | 0.60 | section |
| Hahn–Banach theorem | has application | To | 0.60 | section |
| Hahn–Banach theorem | has application | Moreover | 0.60 | section |
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