Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Uniform_Boundedness_Principle
|
| gptkbp:appliesTo |
gptkb:Banach_spaces
normed vector spaces |
| gptkbp:category |
theorems in functional analysis
|
| gptkbp:consequence |
If a sequence of bounded linear operators converges pointwise, then the sequence is uniformly bounded.
|
| gptkbp:field |
functional analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Banach-Steinhaus theorem
|
| 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 |
A pointwise bounded family of continuous linear operators from a Banach space to a normed vector space is uniformly bounded.
|
| gptkbp:bfsParent |
gptkb:Uniform_Boundedness_Principle
|
| gptkbp:bfsLayer |
6
|