Riesz representation theorem for Hilbert spaces
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Hilbert_space
|
| gptkbp:category |
theorems in functional analysis
theorems in Hilbert spaces |
| gptkbp:field |
functional analysis
|
| gptkbp:hasConcept |
gptkb:Hilbert_space
inner product continuous linear functional |
| https://www.w3.org/2000/01/rdf-schema#label |
Riesz representation theorem for Hilbert spaces
|
| gptkbp:implies |
Hilbert space is isomorphic to its dual space
|
| gptkbp:namedAfter |
gptkb:Frigyes_Riesz
|
| gptkbp:relatedTo |
gptkb:Hahn–Banach_theorem
gptkb:Riesz–Markov–Kakutani_representation_theorem Lax-Milgram theorem |
| gptkbp:state |
Every continuous linear functional on a Hilbert space can be represented as an inner product with a fixed element of the space.
|
| gptkbp:usedIn |
gptkb:signal_processing
operator theory partial differential equations quantum mechanics |
| gptkbp:yearProposed |
1907
|
| gptkbp:bfsParent |
gptkb:Riesz_representation_theorem_for_measures
|
| gptkbp:bfsLayer |
7
|