Uniform Boundedness Principle
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Banach-Steinhaus_theorem
|
| gptkbp:appliesTo |
families of continuous linear operators
|
| gptkbp:category |
theorem in analysis
|
| gptkbp:field |
functional analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Uniform Boundedness Principle
|
| gptkbp:implies |
boundedness of operator norms
|
| gptkbp:namedAfter |
gptkb:Stefan_Banach
gptkb:Hugo_Steinhaus |
| gptkbp:publicationYear |
1927
|
| gptkbp:publishedIn |
gptkb:Fundamenta_Mathematicae
|
| gptkbp:relatedTo |
gptkb:Closed_Graph_Theorem
gptkb:Open_Mapping_Theorem |
| gptkbp:sentence |
If a family of continuous linear operators from a Banach space to a normed vector space is pointwise bounded, then it is uniformly bounded on bounded sets.
|
| gptkbp:usedIn |
analysis of Banach spaces
study of operator theory |
| gptkbp:bfsParent |
gptkb:Banach–Steinhaus_theorem
|
| gptkbp:bfsLayer |
5
|