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".

David Hilbert notableWork
"Hilbert space"
↳ resolves to Hilbert spaces
von Neumann algebras relatedTo
"Hilbert space"
↳ resolves to Hilbert spaces
surface form: von Neumann algebra