Disambiguation evidence for Banach spaces via surface form
"Banach space"
As subject (49)
Triples where this entity appears as subject under the
label "Banach space".
| Predicate | Object |
|---|---|
| centralTo | the study of infinite-dimensional linear phenomena ⓘ |
| developedIn | 20th century ⓘ |
| equippedWith | norm ⓘ |
| fieldOfStudy | functional analysis ⓘ |
| generalizes | finite-dimensional normed vector space ⓘ |
| hasConcept | Banach algebra ⓘ |
| hasConcept | Banach–Steinhaus theorem ⓘ |
| hasConcept | Closed Graph Theorem ⓘ |
| hasConcept | Hahn–Banach theorem ⓘ |
| hasConcept |
Banach inverse mapping theorem
ⓘ
surface form:
Open Mapping Theorem
|
| hasConcept | Schauder basis ⓘ |
| hasConcept | bounded linear operator ⓘ |
| hasConcept | dual space ⓘ |
| hasConcept | reflexive space ⓘ |
| hasConcept | separable Banach space ⓘ |
| hasDefinition | a complete normed vector space ⓘ |
| hasExample | finite-dimensional Euclidean space R^n with any norm ⓘ |
| hasExample | finite-dimensional complex space C^n with any norm ⓘ |
| hasExample | the function space L^p for 1 ≤ p ≤ ∞ ⓘ |
| hasExample | the sequence space l^p for 1 ≤ p ≤ ∞ ⓘ |
| hasExample | the space C([a,b]) of continuous functions on a closed interval with the sup norm ⓘ |
| hasExample | the space l^1 of absolutely summable sequences ⓘ |
| hasExample | the space l^2 of square-summable sequences ⓘ |
| hasExample | the space l^∞ of bounded sequences ⓘ |
| hasProperty | all norms on a finite-dimensional vector space are equivalent ⓘ |
| hasProperty | bounded linear operators between Banach spaces form a Banach space under the operator norm ⓘ |
| hasProperty | closed subspace of a Banach space is a Banach space ⓘ |
| hasProperty | continuous linear functionals form the dual Banach space ⓘ |
| hasProperty | direct sum with suitable norm can be a Banach space ⓘ |
| hasProperty | every Banach space is a Baire space ⓘ |
| hasProperty | every Cauchy sequence converges in the space ⓘ |
| hasProperty | infinite-dimensional Banach spaces can have non-equivalent norms ⓘ |
| hasProperty | is a complete metric space with respect to its norm-induced metric ⓘ |
| hasProperty | product of finitely many Banach spaces is a Banach space ⓘ |
| hasProperty | quotient of a Banach space by a closed subspace is a Banach space ⓘ |
| hasProperty | unit ball is complete in the induced metric ⓘ |
| hasStructure | vector space over the complex numbers ⓘ |
| hasStructure | vector space over the real numbers ⓘ |
| induces | metric via the norm ⓘ |
| instanceOf | mathematical concept ⓘ |
| instanceOf | normed vector space ⓘ |
| instanceOf | topological vector space ⓘ |
| namedAfter | Stefan Banach ⓘ |
| usedIn | approximation theory ⓘ |
| usedIn | harmonic analysis ⓘ |
| usedIn | operator theory ⓘ |
| usedIn | optimization theory ⓘ |
| usedIn | partial differential equations ⓘ |
| usedIn | probability theory ⓘ |
As object (1)
Triples where some other subject referred to this entity
as "Banach space".