Disambiguation evidence for Hilbert spaces via surface form
"Hilbert space"
As subject (50)
Triples where this entity appears as subject under the
label "Hilbert space".
| Predicate | Object |
|---|---|
| hasConcept | bounded linear operator ⓘ |
| hasConcept | closed subspace ⓘ |
| hasConcept | compact operator ⓘ |
| hasConcept | orthogonal projection ⓘ |
| hasConcept | orthonormal basis ⓘ |
| hasConcept | self-adjoint operator ⓘ |
| hasConcept | unitary operator ⓘ |
| hasDefinition | a complete inner product space ⓘ |
| hasExample | Hardy space H^2 on the unit disk ⓘ |
| hasExample | Sobolev space H^1 with appropriate inner product ⓘ |
| hasExample | finite-dimensional Euclidean space R^n with standard inner product ⓘ |
| hasExample | finite-dimensional complex space C^n with standard inner product ⓘ |
| hasExample | function space L^2 of square-integrable functions ⓘ |
| hasExample | sequence space l^2 of square-summable sequences ⓘ |
| hasOperation | inner product conjugate symmetric in complex case ⓘ |
| hasOperation | inner product linear in first argument (in complex case, conjugate-linear in second) ⓘ |
| hasOperation | inner product positive definite ⓘ |
| hasOperation | inner product symmetric in real case ⓘ |
| hasProperty | Bessel inequality holds for orthonormal systems ⓘ |
| hasProperty | Cauchy sequences converge in the norm ⓘ |
| hasProperty | Parseval identity holds for complete orthonormal systems ⓘ |
| hasProperty | Pythagorean theorem generalizes to orthogonal vectors ⓘ |
| hasProperty | Riesz representation theorem holds for continuous linear functionals ⓘ |
| hasProperty | completeness with respect to the norm induced by the inner product ⓘ |
| hasProperty | every closed subspace has an orthogonal complement ⓘ |
| hasProperty | every vector has a unique decomposition into components in a closed subspace and its orthogonal complement ⓘ |
| hasProperty | is a Banach space ⓘ |
| hasProperty | isometries preserve inner product and norm in the Hilbert space ⓘ |
| hasProperty | parallelogram law holds for the norm ⓘ |
| hasProperty | projection theorem holds for closed convex subsets ⓘ |
| hasProperty | separable if it has a countable dense subset ⓘ |
| hasStructure | inner product ⓘ |
| hasStructure | scalar multiplication ⓘ |
| hasStructure | vector addition ⓘ |
| induces | norm via the inner product ⓘ |
| instanceOf | complete metric space ⓘ |
| instanceOf | inner product space ⓘ |
| instanceOf | mathematical structure ⓘ |
| instanceOf | vector space ⓘ |
| isA | Banach space with norm from an inner product ⓘ |
| mayBe | complex ⓘ |
| mayBe | real ⓘ |
| namedAfter | David Hilbert ⓘ |
| usedIn | control theory ⓘ |
| usedIn | functional analysis ⓘ |
| usedIn | harmonic analysis ⓘ |
| usedIn | partial differential equations ⓘ |
| usedIn | quantum field theory ⓘ |
| usedIn | quantum mechanics ⓘ |
| usedIn | signal processing ⓘ |
As object (2)
Triples where some other subject referred to this entity
as "Hilbert space".
surface form:
von Neumann algebra